Trying to troubleshoot a transmission shifting error without considering or examining the internals of the transmission supposedly leading to the error code is not in my opinion the best way to troubleshoot your issue.
I know you want it to be something less involved / messy to deal with. But the fact that this is a physical event occurring inside your transmission to me indicates it is likely a mechanical issue. You've already changed the valve body which was a logical start.
However, the line pressure inside the transmission is critical for smooth shifts as well as ships that occur when they are supposed to. The pcm/tcm sends instructions to the transmission. The question is whether the transmission can follow them.
I suspect something is amiss inside the transmission that physically is not operating correctly in third gear. The TCM seems to be very consistent in telling the transmission what to do shifting into third gear because it slam shifts 100% of the time now.
Take the replacement PCM out of the car and out of the equation. Since you're having issues with it, it just adds one more variable to troubleshooting. Your car runs on the original PCM and it's the only way you can troubleshoot the original problem. With the original parts.
It's going to be difficult to find someone who truly understands this transmission due to its age. Most of the guys wrenching right now weren't born when it was manufactured. You need to find an old guy at a transmission shop you can trust.
Even then, due to its age, they will recommend a full rebuild due to the labor involved in disassembling the internals to get to third gear. The clutch packs are worn out, seals are leaking, transmission fluid pump after this many years could use replacing.. and the dollar figure to do all of this rebuild is probably worth more than the car is worth. I know you don't want to hear that, but it's the truth. You can put a junkyard transmission in it, but with the mileage on it, these taat transmissions, the automatics ALL develop one problem or another as they age. So it's a crapshoot but also a chance at continued life for your vehicle.
There is always the chance that I am completely wrong, but I would not have spent this much time explaining the details to you as to why I don't think I'm wrong. I don't know everything and I don't claim to. I have tried to help many people on several different Saturn forums with every problem under the sun. Transmissions are not my strong point by any means, but troubleshooting is.
Unless you can find someone to evaluate your transmission for free, or evaluate your TCM for free, it's going to cost you money to determine the true nature of the problem, and it's probably an issue that's not financially worth it to fix. Probably.
I believe you have a perfectly good PCM in your car. It plays well with the security system and runs your car in most of the gears. No other whack behavior.
And that's all I have for you.