I have the exact same issue as you. I tried all the troubleshooting and still no luck. I also have the retail GOTY version.

I have re-installed Arkham City 2 days ago via Steam, so I presume to have the newest available version.

(I originally bought the game on Steam shortly after release, and then bought the DLCs over time as they became available, so while I do not have the actual GotY Edition, I do have all available DLC for the game.)

After re-installing the game (had to after I switched my main HDD for an SSD and took the opportunity to completely wipe the system), I ran into the problem that the Trainer Version 03.20.2012 (Steam) doesn't work in-game (no effect) and it causes the game to crash after a few minutes of playing, even if I do not actually use any of it's functions and just have activated it via F1 in the main menu.

I then tried the Trainer for 03.20.2012 (Retail), with the exact same result.

Last, I tried the Trainer for the GotY version 09.09.2012.
And while this one has the definite advantage that it does not crash the game for me, it doesn't have any in-game effect, either.

So now, I am a tad stumped, to be honest. (Btw. where exactly do you check which version you have? The BatmanAC.exe still claims to be version 1.0.0.0 for some reason when I right-click on it in Explorer and look at the details.)

I am on Win7 x64, btw. Tried running Steam, Game and Trainer in XP compatiblity/admin mode, but that didn't help.