Is it feasible to design an audio amp with an adequate frequency response down to DC?
You should be able to do what you want. You need 


A DC-coupled audio amplifier.
No capacitors in the signal path.
Dual-rail supply so the signal can swing positive and negative.


Your other option is to use a H-bridge and PWM the speaker. This is a lot easier to do cheaply than at was a few years ago.