Thanks for all of your responses.
First off, Serra, what you say makes perfect sense. At this point, it's more of a "I want to get it to work" rather than is it feasible to backup my collection this way. For me, I bought a 2 TB drive for $120 which should hold roughly 70 movies. I plan to buy only the movies that I wish to view more than once, this might be around 200 or so, so 3 2TB drives in not cost prohibitive for me.
Also, last night I reformatted my HDD and reran TSRemux and had the same issue. Basically what happens is that Goodfellas starts out with great audio and video in sync for the credits and the opening of when they're in the car but once they get out of the car the audio and video becomes choppy. When I relocate the stream to farther in the movie the video is in slow motion and the audio is still choppy, again, like it's trying to catch up. This is frustrating to me. Like I said, it's more of a personal goal to get this working than a feasibility issue. The movie plays fine from the BD drive and I can't imaging that the HDD would be slower.
Tonight I will troubleshoot more to see if I can just play the original m2ts on my computer. I believe I was able to do this...play it from the BD drive with AnyDVE and without remux and it worked fine. I'd like to say it is something I'm doing wrong with TSRemux, but I have no idea what. There's not very many options, at least in the GUI, not sure if there's a CLI or not.
Wraslor, or anyone else...what is the benefit of using makemkv over TSRemux? Do you think this will solve the issue? I'd certainly give it a try. Is there any difference in quality...my assumption is that MKV is just another container so quality depends upon the formats in the container...but why would that possibly work over m2ts?
Thank you all.