I'm personally testing from a machine that's on dial-up, but I've had another person test it with a broadband connection, and he received the same error. The error is a generic 500, and unfortunately, pair Networks does not allow access to the Apache error logs.
I've setup the script to test for errors issued by CGI.pm, and I'm not seeing anything there. Testing the script on my own machine, I'm able to transfer multi-MB files without a hitch.
Thanks to all who've provided suggestions. I'll give them a go, and post a resolution if I ever get one.