I know my situation is WAY off from yours, BUT maybe it can make you feel better about replacing an ECU..
I was having a random misfire issue on my #4 cylinder.. Replaced plugs, then replaced the coil (e30 w/COP conversion).. Still had the misfire.. I checked everything under the sun, vac leaks, hoses, wiring, you name it..
Did the stomp test for codes and found 1444 which is no codes.. So I went straight to the ECU hoping that it would be the issue and sure enough it was..
After reading your post and seeing that there is no CEL illuminating, that would worry me unless like you guys said, the early model e36s dont have one? But I wouldn't imagine bmw making a car without some way to tell you your shit is blowing up...... ANYWAYS, that's where I would go,, maybe borrow a know good ECM from a buddy and give it a shot.. You may even throw up a post on here and see if any members in your area have a known good you can try..
I'll slosh around this info and see if my little brain can think of anything else it could be,, honestly it sounds like you're doing everything legit and correct,, taking the right steps etc... You got a bastard on your hands, I say good luck to you sir!