Well, the joggler is pretty much a Pi with the display and touch screen already integrated in a nice case (although it's atom based, not ARM) and it also runs linux, so I'm struggling to see what it can't do that a Pi could. You can pick them up quite cheap if you bide your time.
One thing you should check first, though, is that you are driving your amp with enough level to reach its' maximum output. You don't mention it distorting horribly, which leads me to believe there's more to come from it and you just don't have enough gain in the system. You probably need an oscilloscope to see what's happening at the output and how close you are to clipping the amplifier and yes, in my loft...
I have a Squeezebox touch, Squeezebox 3 and an original Squeezebox around the house in addition to a couple of jogglers streaming music from LMS server running on an x86 machine.
Oh, I've just done the controlling central heating with a Pi thing too, so have a PCB design for that if you are doing something along the same lines.
Regarding amplifiers, if you want something cheap that will knock out a reasonable amount of grunt and are happy to do bit of construction work, I'd look for a single chip amplifier. There are plenty of boards on Ebay based on chips like the LM3875 and LM3886 that will be adequate for your application and you'll just need to add a mains transformer and switch it via a relay driven from a GPIO.