Thanks for all of the info guys! I've reduced the hum to acceptable levels by moving things around.
fly135, thanks for those links! I'm going to buy one of those just to play with since they are practicably free
P-90, thanks for the preamp idea. I was thinking about embedding a small TI MSP430 in the guitar and sampling the guitar's output at ~44khz with one of the 12bit ADCs, then send down a digital bitstream (probably manchester encoded data over LVDS) to my amp. Inside the amp, I'd have another TI MSP430 which receives the manchester encoded bitstream and source the AMPs input with one of the 12bit DACs at ~44khz.
Thanks,
Adrian