I think I have the ultimate theory regarding the island "moving". It explains the biggest questions regarding it all. OK. When Ben turned the wheel, the island didn't physically move through time, but rather all biological lifeforms (people and Vincent) that hadn't been converted into being an other lost a certain grounding in the island's linear timeline. The phenomenon must address three groups of people: the others, who basically stayed put in their present time and lived normally for three years until ajira 316 arrived as if the island had not moved at all, those who weren't others (and who, coincidentally or not, had not been on the island for longer than three years) who jumped randomly through the island's timeline, and those on the outside of the island's radius who saw the island "disappear". The fact that Jack, Hurley, Kate, and Sayid were transported from 2008 to 1977, Richard & co. experienced no temporal shift when the wheel was turned, and Charlotte's dead body did not travel with Daniel to 1974 is further proof that the idea of the 815 survivors/Juliet/the freighter folk moving in time relative to the island is more feasible than the reverse: the island itself moving through time.
Richard and the others could have been immune to the temporal shifts for one of two reasons: 1) They are others. Juliet defaulted on her status of being an other, which would explain why she moved through time, but this theory has many holes. Why would a group you associate yourself with have any relevance with how the laws of time travel affect you? Could it be the marking she received in "Stranger in a strange land"? And why wasn't Locke immune? Maybe only others who went through a special ritual at the temple are immune to traveling through time. A better theory is 2) Those who were immune to time-travel are so because they were on the island longer than three years. Perhaps you gain some temporal grounding in the island's linear timeline if you have lived there a while. Or maybe, just maybe, Richard and the others who didn't travel with Locke already moved through time when the wheel was turned before.
There is evidence that it has been turned before. Widmore knew where the exit was when he saved Locke. Ben knew too, as he stored fake passports in a rock near the exit (season 4 deleted scenes) and also knew exactly what to do when Locke said,"He wants us to move the island". Dharma initiative polar bears at the exit in the Tunisian desert, Richard knowing that Locke would be "moving on soon" to give his past self the compass when he patches up John's leg, and Daniel's forekowledge of the Orchid station's powers is further proof that the island moved before and the others have some understanding of what happens when it does.
Perhaps you can only go through what Sawyer/Daniel/Juliet/etc. did when the wheel was turned once in your life for some quantum scientific reason, so Richard & co. fulfilled this quota by jumping through time once before. This theory has holes, too, though, because it fails to account for the others who werent on the island for more than three years. Wouldn't Cindy the flight attendant and the kidnapped kids run into Lafleur's crack team of island hunters if they had traveled with Sawyer to the 1970s? Maybe they were at the temple at the time the wheel was moved and did not travel with Daniel/Sawyer/Juliet/etc. because of that reason. And where is Claire this whole time? Maybe it has something to do with Christian appearing to Locke in ancient island times before he put the wheel back on its axis, as evidenced by an intact four-toed statue seen by Sawyer and co.
The easiest group to explain (ironically) regarding how the Frozen Donkey Wheel phenomenon affected them is the group that actually skipped through time until stopping in 1974. The electomagnetic energy released below the Orchid created some time dilation effect that caused Locke, Miles, Juliet, Sawyer, Rose, Bernard, Daniel, Charlotte, and Frogurt to randomly skip through the island's timeline. I dont know the science here or how it realtes to Einstein's theory of relativity, but I will trust Daniel when he says it would be hard to explain it to a quantum physicist... or maybe its just a TV show. For some reason or another, these people were not immune to taveling through time like Richard was and could not, so far as we know, change the past.
This leaves us with only one group of people to tie the theory together: The Oceanic 6+Desmond+Frank who were not inside the radius of the electromagnetic blast. This part is strange because it has to do with the visibility of the island, which we have been told was not apparent to the outside world. Everytime someone gets close enough to the island to see it, they are ravaged by a storm that crashes incoming vessels(Danielle's science team/Desmond/Naomi/the Kahana science team helicopter/Ajira 316) until they are actually inside the radius of the island that Daniel talked about in the first episode of season 5, where they can see it perfectly; or they approach the island from underwater via a submarine (Juliet and the Dharma Initiative) and cant see the island until they surface at the dock anyway. It seems that the island is surrounded by an outer perimeter that makes it invisible to the outside world until you cross through that perimeter (this could have to do with the electromagnetic properties of the island).
By one theory, the reason that the island can be seen clearly by some of the people entering the island (Frank upon bringing the mercenary team to the island, sayid when he took the zodiac to the island, and most importantly, the helicopter carrying the oceanic 6 when trying to land on the island after the freighter blew up) is because 1) they are following a correct bearing or 2) they have been on the island before. Perhaps the island "disappearing" to the Oceanic 6, Desmond, and Frank is the result of the island cloaking itself to everybody outside of its radius, even those who are following a correct bearing to the island or have been on it before. In this way, the Oceanic 6 are viewing the island when it "moves" as transitioning from being visible (for one of the two reasons listed above) to as if they are google maps trying to see the island, but see only ocean. The island moving could just be the Oceanic 6, Desmond, and Frank becoming like the rest of the world who can not see the island if they are outside of its radius and not viewing it from Daniel's specific 305 degree bearing.
The problem with this theory is that the void left by the "moved" island was filled by water immediately after the light flashed, signaling that the island did in fact corporeally move through space and did not just become unable to be seen. But if the island did move through time or move to another geographical space, why did Richard & co. stay in 2005 when the wheel was turned and experience time linearly until Ajira 316 arrived about three years later, and why did the island remain in the South Pacific between L.A. and Guam? The answer: only the biological lifeforms inside the island's radius moved through time, but the island itself moved spacially to a different geographical location, leaving behind a window in the South Pacific that acted as a portal to the true location of the island. Its like the movie Jumper, where the jumpers teleport to another location, but leave a window to that location open just long enough for Samuel L. Jackson to go through and chase them down. This synchronizes with just about every clue on the show about what happened when the island moved, particularly Eloise Hawking's claim that the island is always moving, leaving windows open that teleport one to the island's true location, but only stay open for a limited amount of time. When the island moved, it did not reamin in the South Pacific (although it did reamin in 2005), but the portal to the island did remain there.
Jin passed through the portal on debris from the exploded Kahana and picked up in 1987 where he would have been had he been on the island when the wheel was turned. The helicopter carrying the Oceanic 6 ran out of gas before it could pass through this portal, but Jack, Kate, Hurley, and Sayid ended up in 1977 when passing through the portal on Ajira 316, where they would have been had they been on the island when the wheel was turned. The Ajira 316 passengers who were never on the island ended up in the present-day because they were never supposed to be on the island when the wheel was turned, so they were never supposed to move through time like Sawyer/Juliet/Daniel/etc. did. The question is whether Richard/Bram/Ilana/Flocke are in the South Pacific or whether they were transported to a different location on earth when Ajira 316 started malfunctioning. It is pretty clear that the Ajira 316 passengers that didnt go to 1977 are in present-day and probably went through some time travel when passing through the window because they went from night to day in a matter of seconds. Whether they are in 2007 or 2008 now is another hour-long article.
The only remaining loose ends are the four wild cards on Ajira 316: Ben, Locke's body, Lapidus, and Sun. Why didn't they travel to 1977 like Jack & Co. did. Ben is an other who lived on the island for 30 years before moving the wheel and leaving, so it makes sense that he, like Richard, is immune to time-travel. Only living organisms can travel through time, as seen when Charlotte's body remained in ancient island time before Locke put the wheel back on its axis, which explains why Locke's body is in the present. But Lapidus and Sun were just like the 815 survivors and freighter folk who skipped through time. Why didn't they go to 1977? The answer may lie with Eloise Hawking's warning that you must recreate the circumstances of the 815 crash exactly. Jack brought a coffin with someone close to him inside, but who he had a rocky relationship with (don't forget Christian's shoes, too). Sayid and Kate switched roles in being the transported fugitive, and Hurley brought Charlie's guitar case (I think). Sun didn't enter the island as she exited it: preganant. Plus, not all of the oceanic 6 were brought back. Lapidus was never aboard 815, even if he was supposed to be, so he could not be a part of 316's recreation, and thus could not go back in time either. It all adds up, unless Juliet detonating of Jughead resets the show and something we haven't thought of at all is the real answer.