Perl does not "merely act as a front end to mv and other command line UNIX commands". the rename builtin never invokes mv or any other external command at all. You might get a significant speedup from running 1 perl program instead of running /bin/mv 16000 times. I'd hardly expect the overhead of starting /bin/mv 16000 times to be the bottleneck here, though.

I've noticed solaris machines getting quite slow with file management if you dump more than a couple of thousand files in the same directory, so if that's what your code is doing, try downloading and unrarring in different different directories.