DD also mostly slept in slings for many months... can't remember when I started to be able to lay her down, to tell the truth. But it was certainly at LEAST 3mo! I and my DH each mastered the art of slipping ourselves out of the sling, leaving DD on the bed still curled up in/on the sling. I do think it's easier to just lay her down on a bed, rather than trying to go into a crib or something.
Most of the time she was in a fleece hotsling pouch, or in an upright carry in my Moby. Yes, you have to re-tighten a Moby every so often, but it can be worth it because it's so comfy. There are other wraps which are very comfy but slightly less stretchy (I later got a Bali Baby Stretch which was just divine) and the woven wraps (girasol, didymos, etc) are also very comfy. Stretchy ones are more forgiving when you're just learning, but the woven ones are *in general* better for the long-term. I sold my Moby when she got too heavy for it to be practical, to another mama starting out with a newborn. No regrets!
Anyway, when she would nap, I'd do something sitting down to rest my back. Another poster mentioned her LO would only sleep while she was standing up, but I was lucky I guess. It certainly can't hurt to try it. I'd, uh, do a lot of browsing and posting here on MDC while she napped, for instance
Or I'd read a good parenting book. Or have a snack. Then do housework when I didn't need a break.
The back-wearing is certainly a great idea. Another thing you might pursue is just to make sure you're really using your carrier properly. If you've got something adjusted less than ideally, it can increase back pain. It shouldn't REALLY hurt to carry baby even for long periods of time, though of course it can... but if something can be improved, it's certainly worth checking.