Resist the temptation! I don't know about the back thing - I've heard their necks can get shortened tendons or something, but even just for the flat-head thing, it's such a bad idea. It's true that most cases of flat-head turn out OK in the end, but therapies are expensive and not always effective. My son's issue wasn't due to a car seat, but long story short, he may need expensive orthodonture down the road and his facial features will always be slightly asymmetrical. Not worth it!
With our second son (perfectly round head :-) we bought an amby sleep hammock. http://www.ambybaby.com/ I have no idea why those haven't taken off more, but highly recommend - easy for travel, cozy for baby. It basically takes the place of a bassinet and crib for about the first 7-8 months.
ETA - you might also want to try different swaddling cloths and devices, or look online for techniques. I was able to swaddle my kids much longer than that. He might need a little time to get used to it, too.