Ah, disregard this one, I think I've got it figured out. I know there are lots of freeware programs out there that claim to do what I was looking for, but they all look sketchy and riddled with malware, so I was looking for a more professional product.
But I just discovered that I should be able to do it in Windows 7 or 8 through the command prompt as administrator. So basic, so easy. If it doesn't work, I'll get back on here with a follow-up.
Here's the command structure:
Open the command prompt as administrator.
Copy your files to your C:\ (its easier on the root, can be deleted afterwards)
copy /b "C:\File.mp4" + "C:\File1.mp4" CombinedFile.mp4
Yeah, that works for some sort of files (like text files) but I found out that it doesn't work for mp4's. You'd have to somehow remove the container and then stitch the individual files and then re-container.
I ended up trying a freeware program called Avidemux. Worked great, very quick. I tried to run the group of parts through a PP export to stitch, just out of curiousity. It would have done it all in about six hours, which is a huge improvement over the multiple days that it took cumulatively to encode the various parts. So PP wasn't smart enough to figure out that it could just merge them, but at least it recognized that no real hard lifting had to be done since the source files now all matched the output parameters. So it was a semi-victory, but Avidemux was much faster.