Thanks, friends! It all helps. Yes, that's a good point--I definitely would need to change my statement of purpose and even my research proposal a little bit, based on the particular school.
And I'll try not to worry about asking my professors to upload those letters again to a different site or organization.
I guess I just wish it was as easy as going to some database, where you punch in your info. Here are my degrees, here's my GPA for each program, this is what I'd like to research, and if it looks good to you, drop me a line.