The tow truck driver at least is right, if the transmission fluid is full and you are not adding fluid, it should either slip all of the time or not at all. A transmission often does begin to slip in one gear or another first, and often until that particular gear is unusable.
As far as the loss of power goes, that could very well be something like the fuel pump or a carburetor, and it might feel as if the transmission is slipping during power loss. I would guess that you need to start with fuel delivery at the carburetors and backtrack to the fuel pump. One thing to look for is an overly rich fuel mixture, which would produce black smoke from the tailpipe(s) and fouled (black, powdery) spark plugs. A simple (but expert) adjustment might solve the problem.
Hope that helps.