My sound card supports hardware mixing. What's the easiest way to use this feature (rather than on an app-by-app basis, hopefully)?
I am afraid there is no easy way. It is probably easier to just use pulse audio for this.
Pulse audio does software mixing, but on current machines doing hardware mixing does not really provide advantages.
I you really want to use hardware mixing you have to look up some .asoundrc options and then use some alsa-pseudo-devices in your programs.