I ended up ordering a rebuilt ECM for about $150, with a $45 core. I figured it was worth $100 or so to just swap it out. It is on the way.
In the meantime, I was able to do the EEC-IV test.
For Key On Engine Off (KOEO), I received two codes at first: 24 and 67. After a couple of repetitions, however, the 24 fell off, so I was only left with 67. My manual shows that KOEO code 67 is "Neutral Drive Switch (NDS) circuit open/A/C on". What does that mean? I made sure the AC and all interior electronics were turned off.
I did not receive any Continuous Memory codes.
Strangely, or perhaps due to the ECM damage, I was not able to get the test to work with the engine running. I tried several times.
The idle is still around 2,000 rpm. Hopefully the new ECM solves the problem.