Update thus far, not fixed, but fixed something. New code C1805, Mismatch PCM and/or ABS/TCM module. Not a VIN mismatch, but still a mismatch fault. But I have learned a few new things for IDS. As far as I can tell, everything is programmed and set with the right VIN. I tried looking to see if I need an ABS from a manual transmission truck, but I can't find any ABS modules that specify whether they are for manual or automatic, so it doesn't look like there should be any mismatch from the part numbers, but maybe I have to try that.
So VIN mismatch is solved, I think...
First, I found a post mentioning that the ABS needs to see a complete ignition run/stop cycle. So I started the engine, then turned it off, and let the truck sit 15 minutes before turning the ignition back to on. Turned the engine on and cleared all DTC's, then it only showed ABS fault B1596-E0. I started the engine, the ABS and TCM dash lights turned off, then back on. I checked the DTC's again, and ABS was back to showing mismatch.
I tried reprogramming the ABS in Programmable Module Installation to set the ABS to the old VIN from the PCM I have now. Maybe if the ABS is reading the other VIN, I can just make the ABS match. That didn't change anything, so I tried reprogramming back to my correct VIN. That session crashed, which is apparently common in IDS, so I got to learn how to install As-Built data. Yay. Fairly easy really,
https://www.motorcraftservice.com/AsBuilt - just type in your VIN and you'll get a list of Hex codes that you have to type in. It takes a while and you want to make sure the battery has a full charge, but just follow the prompts and IDS will tell you which line of code needs to be typed in where. IDS finished the As-Built programming with no problems, but ABS still showed a mismatch.
The other forum thread mentioned removing the old session files. Older IDS versions might have had the Sessions folder in C:/Programs, but now its in the hidden ProgramData folder under Ford/IDS/Sessions. Don't delete the folders or the metrics file, but all the session files that start with VIN numbers can be deleted or archived in a separate folder. I tried this first before doing another no-key PCM reprogramming. Start a new session with the key out of the ignition, run through the entire setup and data entry with no key. IDS won't ask to pull data from previous sessions, because there aren't any session files. Don't put the key in or turn the ignition to On until the program tells you to install the new PCM module. Everything seemed to program correctly again, but the ABS still throws a VIN mismatch error. I think this actually fixed the VIN issue, but I didn't realise I was getting a new code now for just mismatch instead of VIN mismatch.
Finally, I deleted the session files from ProgramData again, just to check and confirm what's programmed on the PCM. Started a new session with the key on, with no previous sessions available to restore that might give data that wasn't actually programmed to the PCM. The VIN check on the new session was correct, and under Powertrain - OBD Test Modes - Mode 9 Vehicle Information shows the correct VIN. Then I went to Programmable Settings - Tire Size and Axle Ratio shows the correct tire and gear ratios that I programmed. Clearly the PCM was programmed and has the correct settings.