That might be a good question to ask on the Handbrake forums. Yeah I'm sure the signal to noise ratio sucks, but you'd get an interesting thread going with a title like "$1k budget, what is a killer encoding rig", you'd just need to filter it for junk.

While Handbrake/ffmpeg can use multiple cores, I'd assume that at some point the rate of improvement slows down, but maybe that would require a pair of Bulldozers.