i hate cPanel (or any other sys control system). I know it's useful when you're managing dozens of sites but i still hate it.
You could try writing your own php script to do a mysqldump. Mysqldump has lots of flags and parameters you can set in order to change the verbosity of the output.
You could call mysqldump from within PHP using [man]exec[/man] or [man]passthru[/man] or something like that. If you choose the right flags, you can have dramatically different output.
Another possibility is that your PHP script to export manually is slow because it writes a single line at a time. You could try creating a string variable to buffer your output and only writing the output file every 1000 lines or something. Fewer writes to disk should be significantly faster. Depending on your PHP setup, you may be allowed enough memory to dump the entire thing to a string before writing it out to a file.