My bad, I worded that last part poorly. Right after recording, the other tracks sounds like they're all about the same volume or louder than the drums, but the drum tracks are the only ones that clip. If I lower the drum track levels with the master fader in EZDrummer to stop the clipping, the drums end up being too quiet. The other (guitar/synth) tracks stay at a listenable volume, but don't clip.
I hadn't done any gain staging at the time I made my initial post, but I did try reducing the input gain on each individual drum track to put the peaks between -6 and -12dB in the loudest part of the song. This caused the same problem of making the drums too quiet.