I have a quick question... Where did you acquire the 2tb hard drive? and how much was it? I'm also guessing that it is a SATA drive and you used some kind of converter, but I may be wrong... I know that I'll be little help in helping with your problem, as the biggest hard drive that I currently have is 150gb, which can obviously fit only about 30-40 xbox games...
My guess would be that you must have partioned the data correctly, if you had 200+ games working before hand... What new games were you loading on that didn't work? It could possibly be coincidence that you have reached around 250 and then placed a couple of games on that may not be compatible with your dash. A long time ago I was going good with my games, then I tried to put on stubs the zombie and a harry potter game, and neither of them worked. I thought that I had too many games, but then I put on darkwatch, which worked like a charm. Just an idea, but I'm sure you've already ruled that out in testing. Plus if you are deleting certain saves, then it is completely likely that your games may not load. I'd suggest deleting the entire folder in your udata/tdata that pertains to individual games. Though for some reason it does not seem to me that new games would be affected by there being too many saves, unless you have used all the room on your E drive...
Another possibility, which happened to me once. Was that my cache files were becoming too large, possibly a problem with soft rebooting, but I have no real idea why. Where at times I had to manually delete the cache files that were stored for playing a certain game, before others would load. Could be a single case problem on my end. Those files were located on my Z drive, though it could be different for you...
Sorry that I couldn't really be of much help, but if you can let me know where I can acquire a lockable 2tb hard drive that works, I'd be very appreciative. Also I live in Australia so it might not ship here, but i'll cross my fingers..
Good luck fixing ur issue.