Well, we did it! I spent $195 at Petsmart on Saturday purchasing a new 20 gallon tank with stand (they didn't have any 29's in my price range). We put the stand together today -- took us three hours -- and I set the tank up and moved the guys in. I scooped out about a cup ful of gravel from the cycled 10 gallon and poured it into the new tank.
I also took the filter cartridge from the 10 gallon and stuck it in the filter for the 20 and just kind of squeezed some of the gunk out of it, hoping to jumpstart the cycle. I checked the water, but had no readings of any sorts (except a little nitrates that our well water has naturally).
We added a couple catfish, who already have been busy chowing on the gunk that came from the old tank.
My only problem now is that the divider I bought for the 10 gallon is clear. The two bettas can see each other and they spent most of the afternoon flaring at each other. I put some plants in front of the divider, but they aren't tall enough and they can still see each other. I considered buying one of those tank background thingys, but then the waterflow would be blocked. Any suggestions?
I'm going to check the water tomorrow. I'm a little worried that now I don't have enough fish to do a good cycle, so I might order the bio spira anyway.