Looks like the Rhythmik L12 is a great sub... and it does (just barely) fit! I can manage a little over 15", maybe 16", in depth and height. I'll triple check the measurements before buying anything.
Any other recommendations?
I see that the SVS SB-1000 should also fit, and people in these forums have recommended other SVS models, usually the bigger ones.
And yes... vibration. It's a heavy cabinet of solid hardwood. Rubber feet will help a little. Even so, there will be some inevitable resonances. Will it be worse subjectively than having no subwoofer, and losing a lot of the sound below 60 Hz?