I only found one registry entry per EP that was about the install folder and needed changing when I moved my folders around, so it might be quicker to do it that way
I didn't quite do what you're doing - I just got a bigger drive which I partitioned into two drives of different sizes, uninstalled every game bar TS2, copied everything into the small one, and then moved documents and TS2 onto the bigger partition. The reason I reinstalled everything but TS2 is that changing the million cds and dvds would have been more trouble than editing things manually for this game, and even an installation like that is way less trouble than what you'd have to do, so... XD
I never patched anything, as far as I can recall. If the 'updating your game' thing actually does nothing, then I've always played an unpatched game and sorted out anything I deemed a bug with third-party fixes. It's worked for me for all these years, and if it worked for you before you may as well carry on.
I don't know anything at all about the EA Store, though. Sorry
Good luck with all this, whatever you do!