Thanks for all the ideas, folks. I thought of the slide-out option too, but my concern was I wouldn't be able to make it as large as I wanted to given the front wheel well. My other worry is I don't want something I HAVE to fold down to get out, because if you end up parking somewhere without enough room to do that, you're kinda stuck. ;)
I may give a go of having something double-fold. It would be hinged/supported along the side, but then it would have a second hinge along the front edge with a small section that would come down in front of the entry door. I have a hitch-mounted cargo carrier that does this with two bolts and a small extra section meant to form a ramp - I'd just keep that bit flat. Something like this:
Wheelchair and Mobility Scooter Hitch Carrier - Aluminum
Next question on the planning front - has anybody ever cut down their wheel wells to get a small amount of extra floor space above them? Just from eyeballing photos it looks like there's a lot more room in there than I have, say, in my car. I'm not sure what top clearance above the tire is actually REQUIRED but it seems like if some people are fine putting on bigger tires you ought to be able to do the opposite and take an inch or two off the top...