Who has taken an official WotC module like Lost Mines of Phandelver, Rise of Tiamat, or Curse of Strahd, and rethemed it to your own world, either from scratch for those adventures, or to use them as a story arc in a long-running campaign?

I'm considering using Tomb of Annihilation for a plotline to a lost temple on a lost continent I have planned for my campaign. But if my players choose the frozen wastes, what is better, Storm King's Thunder or Rime of the Frostmaiden.

Note: I run a fairly deadly campaign. Only two original PCs remain. Some players are on their third character and we're only level 6.

To the general point, people do that all the time.  Whether it's a simple reskin, or plopping it down in your world contextless, to a careful integration and reworking, to just playing the adventure with little regard to the world it's set in.

So of the three Tomb of Annihilation is considered the most meat grinder-y of the options you've presented, plus in Chult your party could get sidetracked and become intrepid dinosaur hunters.  If you make Chult your "lost continent" you can.  It's not quite "lost" and there is some established FR realms presences you'll need to negotiate but they're all easily reskinned.  Rime of the Frostmaiden is probably easier to drop into an established world as it's set in a relatively isolated and geographically limited area, I haven't run it or adapted it yet but some say it's a bit "weak" in terms of actual threats to your party.  Storm King's Thunder might be the toughest to just drop in as the terrain it covers basically starts with a line that starts roughly at Waterdeep and extends east across the continent.  Then everything North of the line is at play in that adventure (the Tiamat adventures are similar in scope, but I think Storm King is a better work, so good choice though not the best fit).  So given that it's the most "grounded" in the Forgotten Realms so would put a burden on you to integrate into your established world, unless your lost continent turns out to be the Realms anyway.  That said, there's some great ideas in Storm King's you can run with if you want to make giants a presence and force in your world.  

From what you are saying I'd probably lean towards Tomb of Annihilation if they go towards the Sun Temple in the south, Rime of the Frostmaiden if the go for the Thunder Pillar in the northeast. It sounds like I could potentially integrate Storm King's Thunder, by just skipping some low-level chapters and switching around some of the plot hooks into the later chapters, but it would be more work.

My world is completely homebrew, no connection to published stuff except sharing most races, monsters, spells, etc.

Yeah, like I said ToA and RotF are both easily "dropped" into available space in your world to play.  There is a sort of meta plot point to ToA regarding a crisis pertaining to resurrection magic that gives the adventure its purpose, you may have to rejigger that to something that fits your world.   RotF is "it's cold and dark, and it shouldn't be _this_ cold and dark" and requires less integrating in that way (and having literally re-read the lore of Levistus, their scheme in Icewind Dale could happen anywhere it's cold on the Prime Material Plane, and Auril is easily reskinned to whatever pantheon your world or that region accepts.  Storm King's Thunder I'd suggest reading as inspiration, because it's really a defined world exploration adventure with Giants showing up for the big set pieces, so you'd be left doing a lot of remapping.  Just rating them as adventures, my ranking would go SKT, ToA, RotF, but given your particular situation I'd go either ToA and RotF, and maybe read SKT and adapt that as the next big campaign while running one of the other two.