OK, what's the biggest horizontal flat area that you have? How big is the quilt? Do you have anyone who could help you (e.g. by temporarily moving furniture, or at least just helping get the quilt smooth and taut)? I'm pretty much housebound myself, I know what it's like. What limitations do you have that would affect basting? Many people don't get on well with crawling around on the floor, for instance. That's one of the biggest things for me, as well as fatigue kicking in before I've finished.
If you have a double bed, I'm wondering about using that as a basting surface. A mattress isn't hard like a floor, but it might be manageable, especially if you can get someone to help. That plus a basting spray (I haven't used one but I hear good things about them - no idea how they are if you have chemical sensitivities, though, it's one reason why I haven't tried one) might work quite nicely, if you can get to all the bits of the bed to smooth out the layers.