Just an update. I figured out by banning my own MAC address on the old router, restarting everything (all computers, too), that I was able to connect exclusively to the N router. This also allowed me to change the radio broadcast to N-only instead of mixed, which theoretically increases the strength. I didn't notice a difference in the latter, since it was really strong to begin with, but it's got to be worth something--if anything, the signals don't compete anymore.
If anyone has found a better idea than banning my MAC address, please let me know. I don't know if this causes performance issues on the other router or not.