I think you have two flaky RCMs. I'd almost bet money on it.
The only way to know is to have DJ rebuild yours OR put in a NEW one.

RCMs are FAMOUS for doing just what your car is doing. The BIG TEST is to turn the key to "START", if you get no starter engagement, release the key to "ON".
If the engine cooling fan warps up to high speed in about 30 seconds, the RCM is bad. PERIOD.

The fact that it started and then died using one of them, after you messed with it, even reinforces that it's the RCM..