I want to take the Fantastic Fan in the cabover, which is an exhaust fan only, put it in the bathroom and replace with a reversible fan in the overhead. I remember a fan I had in my Arctic Fox that...
Why don't you just put the reversible switch into the Fantastic fan? That is a whole lost less work and money than swapping it out. The fan is the same except for the switch. While you are at it you can put in the three speed switch (and the thermostatic control if you like).