While I have not done such a thorough job as OP (wow, you're so patient for sticking through all this!) I am experiencing a similar problem. This has happened to me more than several times throughout multiple updates.
1. For me, it started happening again after the basegame + lovestruck update. Since then I have had two separate cases of this.
2. Like in OP's case, I click Play on Steam, it thinks for a bit, then resets to Play again.
3. Both times I have run a verification of system files. It said some files were broken and apparently redownloaded (what is even funnier, the number of files was different every time, something like 28 and 4). That didn't help. Except this time it also asked for admin permissions (granted) upon launch. Then it reset to Play again.
3a. I had first blamed it on my mods, which is totally logical since they break after every patch, so I HAVE removed Mods and cleared the caches.
4. I read somewhere that the EA app was broken. So I went on to open the EA app manually. When I pressed Play in Steam, it tried to bring up the EA app, the app said there's an error, I reloaded it somehow (don't remember exactly), and on the second try the game actually launched.
5. A couple days later (obviously my computer was restarted since then), same issue. This time repairing files through Steam and launching the EA app manually didn't help. Same issue. So I downloaded it, it gave an error on launch, and suggested I restart. So I did and this time the game worked. Now folks, if you don't do a restart at this step, it will not fix itself.
To reiterate:
1. Occurs sparingly, but is extremely annoying.
2. I have definitely tried launching without Mods. I have cleared cache files.
3. Since I have found a workaround, I will not be reinstalling my whole game. I will not be gathering files, creating new saves, anything else. This is informational for other users who encounter this issue. I will not waste my time standing in for EA's quality control which are apparently so overworked and underpaid that they did not test the basic functionality of actually launching the game from a platform that brings the company millions.
