So, since it's gotten some hits in "Sites I Want to See" and my post for "Quick Interest Check" was getting long, might as well take a shot at being able to drag myself to making this idea a bit more of a reality:
Central concept is an isekai-styled setting (person ends up in another world blah blah) but I want to play with one of the things not played with a lot in the power-fantasy kind of driven set-up most animes tend to take it: transformations. Sure, they tend to maybe discuss things like maybe a change in class, but there's so much other stuff that could be played with, especially regarding fantasy species, gender, etc. Like, going from a human to an elf is very "Meh", but human towards something like dragonborn (not Skyrim), a beastfolk, stuff like that would be a pretty big change, and the ability of this kind of set up to explore concepts of gender identity and fluidity is usually glossed over.
The main sort of hook for the site that I thought of that would really let this idea of adjusting to a new life, no matter how widely it diverged from your old one, is that much of the character sheet is "randomized" for your "new life". However, you as a player get to pick a few things to set it in stone as you wish, but not enough to have complete control over what you end up being. I think that brings up interesting questions for the players, too: what are the most important things to your character? Obviously the character's past history and personality are up to the player, and age probably can carry over (discuss below), but things like species, gender, background, etc. could all be up in the air.
So, just going to split this up into a few things to discuss:
Setting
Most isekai tend to be set in a fantasy setting, maybe throw in some light RPG elements (also discussed below), but nothing about this idea requires a fantasy setting. Technically sci-fi could work (alien species are still species), but my preference is a bit more towards the fantasy setting. Presuming players are from a relatively "present" time, that change to a more fantasy setting is just another hurdle to adjust. Or we could shake things up a bit and have them in a modern fantasy setting. I'm flexible on both, really. The main advantage of doing fantasy over sci-fi is the scale can be kept kind of small (one kingdom or city or whatever) while still also having a variety of races to really get to play around with the transformation idea a bit.
Edit: So, someone over at RPG-Directory had a suggestion on the setting that inspired a potental site plot if we do this sort of mixture of fantasy/sci-fi. Below is their comment and my response.
Genre
Since my interest is primarily in having players deal with their characters setting up new lives that are widely divergent from their own, I'm kind of more interested in doing a more slice-of-life deal than a high fantasy dungeons-and-dragons kind of deal. Sure, some elements of that can be included (I mean, if you woke up with giant fangs you might be interested in giving a try), but focusing on raids or quests and adventures feels kind of distracting from what I had in mind. This feels less of an issue in a modern fantasy setting, where I guess the tone would be almost more like Beastars, perhaps, in terms of world-building (oh god I will need help with world building).
Character Creation
Players would be given full control over personality and past lives of their characters, but their new lives would be up to chance, basically. The main things to work out is how much is randomized. With a fantasy setting, species is an easy one: could end up a human, or maybe an elf, beastfolk, whatever! Gender is a harder one since hard-set male/female binary isn't quite a "thing" (I mean, part of the point of this would be to explore gender identity after all) and all the politics of the real world surrounding these issues, but I still think there is a value in exploring stuff like this. I'm just aware it'd be the trickiest one to probably present and discuss (note: I would not have orientation be a part of the randomization but leave that as something for characters to explore on their own).
Background might also be a tricky one, but more in the work for it. My thought was to have a database of general "prompts" for character backgrounds and give players at least some leeway in generating how their character fits into the world (I am assuming that their age would carry over, leading to a sort of mixture of their old lives and "new" lives being intertwined in their memories) as long as they don't stray too far from it (like, if they got "born into a low-income family, they obviously can't write "then I won the lottery" or something).
RPG Elements
If we were to include RPG-elements, I'd want them to be relatively light. To that end, something like Dungeon Worlds (a Powered by the Apocalypse -based system) would be my preference. It's more developed towards interactive story-telling and has less in the way of dice and stats: you have moves that represent "things you can do", roll 2d6+modifiers, and you can get a fail, mixed success (you do what you want but at a cost), or you succeed. In theory it should be more streamlined, and would work really well I think for this kind of deal. Best thing is the system is pretty flexible (lots of settings, books, etc. covering everything from Cthulu to super-heroes, and even a Twilight inspired one) that an original system can be developed as time goes on.
If developed, however, would need "playbooks" representing different classes (ex: in Dungeon World thieves have a "move" representing the ability to pick locks) , and each species developed would probably need some unique moves (ex: in a Dungeon World campaign I have a lizardfolk character that uses some moves from a third party "Reptilian" playbook to represent things like attacking or using the tail like a third limb). So there's a lot of additional work that would be needed that I don't think is necessary but is an option if people want to go more classic "trapped in another world that just happens to have RPG mechanics" deal.