Building a bike from new components is usually more $$ than a complete bike, used stuff you can do it cheaper but it takes longer and can be hit or miss. You could build a cyclocross bike for that much but it's just a matter of hunting and pecking finding the right stuff. Or you could try a mail-order bike like an Ibex, they used to have a really cheap cyclocross, now they just have a really cheap flat-bar road bike:
http://www.ibexbikes.com/Bikes/COR-CT-Details.html
it may accept cyclocross tires, I don't know. They also sell just frames, which are pretty cheap. Nashbar frames are decent and reasonably priced too. Anything new that's a step up, like Surly, will cost about $400 for the frame compared to 2-300 for Nashbar/Ibex/Bikes Direct (chinese made) type of frames. It can be hard finding used frames w/ canti brakes studs for 700c tires because that's basically either a touring or cyclocross frame, and both are niche products.
If you decide to piece something together in the interim you could just put some v-brakes on your current ride.
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fun facts:
Psychopaths have trouble understanding abstract concepts.
"Incompetent individuals, compared with their more competent peers, will dramatically overestimate their ability and performance relative to objective criteria."