Sounds like CKP but don't believe it is with the other symptoms.

P 0107 is a MAP low signal code.
Have you checked the voltage on it? I believe you said you cleaned it but is it putting out the right voltage? By definition, the code wouldn't set if it was. That would seemingly wreck your air fuel mix. Can't say by how much because I don't know what it's reading.

Also check wiring. Could be even more simple since the code does not go away.

If you can keep it running off spray, check the vacuum level.

Running at 2500 RPM after 10 minutes is not normal unless your foot was involved. That sounds more like a vacuum leak. Maybe at MAP?

Should be able to monitor map and vacuum w scanner with real-time data capabilities. If you can get it to run.

If you have spark and fuel, the CKP is not at fault at that exact moment in time. No CKP signal equals no spark plus no fuel at injectors.

Have you checked all of your IGN fuses? Sounds silly but stranger things have happened on older vehicles with thin film corrosion interrupting circuits in the fuse box

After you shutoff (no more coolant flow) I found out the CKP warms up yet more from the hot muffler because of where it is situated. “Half hour later” was the point where all three of these Saturns failed to start although they would restart again right away (ie within ten minutes) or after an hour or so.

One of the Saturns (a 96 automatic sl1) would be out on the highway and start running very crummy. After pulling over it quit and wouldn’t restart until cold. In all cases there wasn’t even a code to give the indication. They all behaved differently performance wise too.

When doing errands my cars are usually stopped for five minutes and at night or for lunch those cars mostly got cold enough before the next trip. The first CKP was the toughest one to troubleshoot. My mechanic at the time changed it when all else failed .. finding it hard to remember to go out and try starting after half an hour .. so he knew what I meant.

Only ever had one person in about 17 years post that they actually got a CKP code.

If you absolutely must know, pull the CKP and measure its resistance when cold. I believe the spec is 500 to 700 ohms but I have to look it up to be sure.

The time dependent nature of being able to restart the vehicle scenes to possibly point towards the CKP but I have my doubts.

​​​​​​Have you confirmed spark and fuel while someone else cranks the engine when it won't start? Does it fire and not start or does it not even fire?