Avoid the chinese fans on ebay. I replace them for guys all the time with bad, noisy motor bearings some only last a year or two max. Use a quality fan like a Spal. They are made in Italy and are a tier 1 oem supplier.

You could run a pusher fan on one side and a puller on the other and just switch on the one that is needed depending on direction.

How do you make sure that you get enough air when running backwards? Could you make an air duct with a flapper valve that could pick up cool air somehow?

I have one that I have run in a car for 10 years with no problems.