Nice looking project! (Really like seeing the felt!!!) I hope you post more info & measurements.
Now, please define "inexpensive." And maybe add something about how much fidelity you're hoping for. Unfortunately, ASR is still looking for a cheapish amp with >100dB SINAD...
"Prebuilt for less than Neurochrome" probably includes
@March Audio's 2x75w Ncore, at around $1500 for 4 channels. In the US, the 7x200W Monolith might make sense for $1600, because it could drive the woofers, too. At the lower end, Emotiva's 5x80W is $500, though it's almost certainly not as clean.
Used amps increase your options, obviously. Amps with 5-7 channels from Adcom, ATI, Outlaw & Parasound are often pretty cheap on Ebay. And the Crestron 12x60 (basically an ATI 6012) or 16x60 are often REALLY cheap, especially if you can find one for local pickup. The Crestrons require some minor modding. (I bought a 12x60 with poor cosmetics for <$20 channel, shipped. And that's hardly the best deal I've seen.)
Finally, since you're triamping, what's your source?
@Cosmik can tell you about using older receivers here, which can be CRAZY cheap. PC DSP -> HDMI -> used AVR is probably the lowest-cost avenue.