I have a modern steel bike with long reach calipers that fit 32mm, but $300 is a pretty low budget. I would monitor CL constantly; the better the deal quicker people tend to jump on it.

Also regarding the clearance picture above, make sure to consider the clearance from the seat tube as well. I have a bike which its rear brake looks like it can clear 28mm, but the space between the seat tube makes it incompatible.