Hi Pete,
FWIW:
My memory is getting fuzzy, but I had an '85 Camry w/ the I-4 that had a similar problem. I busted my ass trying to fix the problem before I found the solution.
YMMV, but my old car had a small pick-up coil inside the distributor that sat on the vacuum advance plate (forgive the terminology - it is probably not correct as my memory of the problem is fuzzy). One of the small wires leading to the pick-up coil had a break inside the insulation. Every time the vacuum advance plate moved (i.e., every time I hit the gas from a stop), the wire flexed and I would get a momentary open circuit, thus cutting the ignition to the engine for a split second. Then, the wire strands would come back together and the engine would kick back in.
I won't tell you how many other things I replaced/"fixed" before I found my problem.

As I recall, the part was not cheap!
Good luck!