Two things come to mind since we're talking about a mono amp instead of a stereo amp, albeit one with lots of headroom.
First, DIY subwoofer, especially a stealthy, infinite baffle thing. Build it into the closet, floor or ceiling, throw a grate over it, and you'd have the benefit of additional subwoofer capacity and linearity for the cost of a couple drivers and plywood.
Second, distributed multi-zone mono audio. Combine the stereo signal at the line level, feed it to the amp and send it to 2-4 ceiling-mounted or outdoor speakers in places where you'd like to have some music but don't care too much about imaging.
These may not be technically viable suggestions. I'm just riffing from a user point of view. You'd need somebody smarter than me to ensure proof of concept on the technical architecture.
I do like Bruce's hoverwoofer idea, though. How about some combination subwoofer and robotic vacuum cleaner - the Boomba.
Good luck with that.
