First, do your ten days include the days you fly in, and then fly out? In that case, you will have only eight "full" days in the region. But whether eight or ten, it seems barely enough for even one of these three countries, to say nothing of three. A few other things to think about:
 Do you have experience driving outside of North America or Western Europe? If, lost and confused in a Central Asian city or town, you cause a bad collision, and find yourself surrounded by justifiably angry locals all yelling at you in Uzbek, would you be able to handle the situation?
 On a related note -- do you speak any of the local languages, or perhaps Russian (which, according to what I have read, may still be useful in the region)?
 As for sleeping in your car -- it's not really a question of how comfortable you will be, but how safe. I suppose the neighborhoods around "fancy resorts" are safe enough to park and sleep; you will need to find out, and fast, how safe it may be to do this in Central Asia, whether on remote roads, in small towns, or in cities. Keep in mind that if you do have trouble "camping" in your car, it may be from the police. (There are many cultures -- I don't know whether they include those in Central Asia -- where "most anything goes" is not always as popular with the local people, as it is with footloose tourists.)
I'll add that I've found the Islamic countries I've so far visited (West Africa, Turkey) to be generally safe and hospitable, but I haven't been to Central Asia and so can't personally affirm that it will be the same. Finally, if you haven't done so, you may want to do some of your research on the TripAdvisor forums, where you may get more expert advice. This one tends to attract mainly Europe-oriented tourists.