Caveat--I'm not an expert--but I would suggest the following to do first on
your rough idle problem. First, because it's cheap, and second because
nothing will work right if there's a problem here. A. Check/replace all
vacuum hoses. Especially the large ones near the engine block, under the air
flow meter/air filter bucket. Use clamps and sealer to make sure there isn't
any vacuum leak. This could cause the problems you're talking about in
itself. B. Check all grounds. Make yourself a "ground web" that connects
both cylinder heads to the block to the ECU etc. Both of these items should
cost you less than $25. Once you've done these two things, move on to the
more expensive stuff. Don't automatically "blame the computer" (or other
electronic components) until you've eliminated all other potential problems.
Again, if there is either a vacuum leak or a bad ground, nothing else you do
will solve the problems you're describing.

Save the expensive, hard stuff, like pulling the engine, for last. I always
think of doing a complete rebuild to solve a misfire problem, only to find
that the rebuilt engine does the same thing--because there's a fault in the
wiring harness, or whatever.

Good luck and keep us posted.