I've known MANY people who swear by the odor control of Yesterday's News cat litter as bedding. It's only suitable because it is paper based as you said, other cat litters are NOT safe to use. I'd recommend trying it just because I've heard so much good of it as far as odor control ^^
My rats HATED Yesterday's News (so did my cat, incidentally). The texture of the "small animals" YN is not that much different from the cat's. I use Kaytee's comfort bedding. Also, my favorite thing to use which controlled odor even better than the Total Comfort was shredded (unbleached) paper towels! My dad works for an elementary school, and he put packages of those through a shredder for me. The rats loved it, I loved it.. a very cheap win-win situation!
I had the grey carefresh for a while and Giz (I had her by herself for a few weeks) sneezed like mad. Other than the sneezing, nothing was wrong with her, no discharge, eating, drinking, playing fine, etc. I switched her to the Carefresh ultra to see if it would make a difference and voila, no more sneezing! Now I have 3 rats in a small-medium cage and I end up cleaning it AT LEAST every 3-4 days though. But I do like the carefresh ultra. by the way, I'm looking into getting them a bigger cage.
Aspen is by far the best in odor control IMHO. It's also much cheaper than other types of bedding (141 liter bag of aspen cost around $16 at petco, 10 liters of recycled paper cost around $8 at petco,$4.50 uncolored at Wal mart).