Pics are awesome .... The first one is my favorite!
Sorry to hear about not being able to solve the problem. Maybe I could help if you list all the things you changed and the behavior before and after (if any difference).
Knowing that you already have the m20 in the bay, minus EFi, swapping in a late model m20, be it b20,b23,b25 will be relatively easier than going from m10 to m20. Just make sure you don't get an early model with the crank position sensor in the trans bell, try to source one from a post '87 e30 or an e34.
Basically the hardest thing is the fuel return line. You need to route it correctly and check if your tank will accept it. If not - you need to figure out a way to solve it. In our case we were lucky to start with a 323 shell, so it was readily available and I don't know what exactly is involved on this end. I can ask my more informed buddy and post another reply later.
Otherwise, you need to splice the engine harness with the chassis harness. Yours should have the square connector in your car, even if yours is carbed there still is some wiring. What I'd recommend is remove the square connector from the chassis harness and replace it with the late e30 style C101 connector. You will make your life easier for the future, if you swap harnesses or even swap in a different bmw engine. I
think you will need to add some fuses for powering up the fuel pump and O2 sensor relays.
You need to relocate the battery to the trunk, an e30 cable works fine, you need to figure out how to make it not move and where to put the ground strap.
Radiator from a 325e fits perfectly, same model water pump, expansion tank and water hoses. IIRC the top and bottom hoses need a tiny bit of shortening to smooth out the kinks due to some tighter clearances in the e21 as opposed to e30s.
Basically that's it. Use your own motor mounts, your own flywheel and clutch assembly if they are good, and the existing transmission, shifter and driveshaft.
I'll try to find my buddies notes from when he swapped his, but again - he started with a 323i shell, so the return fuel line and fuel system was readily available.
In the meantime, you may find this board very useful too.
http://www.todor.info/repair/e21swap/