I'm not quite sure if the transmission could affect the ABS system/module... I have a similar issue and am also leaning towards thinking it is the ABS module that's crapped out somehow. When I bought my '04 GTP I would get the Service Variable Effort Steering message in the DIC every time I'd start the engine; I eventually took it to a local dealer for a diagnostic and I was told ((I don't know WHAT he said about the EBCM and the rack because he spoke way too quickly)) I needed a new rack and pinion - which eventually I ordered one online (definitely not buying anything from the dealer) and had it replaced but to no avail. The mechanic actually did mention something about a code for the left rear wheel but I don't remember what it was. Actually just a week after going to the dealer, every single day after a while of driving (maybe 10 minutes or so) and several times a day, I will get two beeps and notification in the DIC that traction control and stability control have turned off, then followed by the warnings each time to service traction system, stability system, ABS system and brake system. And sometimes it forgets to mention the variable effort steering message but it will maybe 5 minutes later, lol. I really think (and hope) it is the EBCM that is in need of repair or replacement (I read somewhere someone will repair it for $99 if you ship it to them which is not terrible, unless you find a fully functioning one that matches your vehicle in a junkyard for less). I'm kind of pissed I replaced the rack for nothing (and I actually found out afterwards that the previous owners had already had it replaced a year before!)
Oh well, trial and error I guess, and believing idiots at dealers who want to rip you off. (they wanted to charge me $1,900 to replace the rack... )