I found this thread while super-searching on another Socket question I had, and realized I never updated it with how I ended up achieving this. I user Data::Dumper to flatten the hash into a scalar, sent that to the server, then used eval to turn it back into a hash, and it worked flawlessly.

Of course now I'm trying the educational task of creating a two-way client-server app using IO::Socket without going back and copy/pasting a bunch of code. I'm learning much more this way, but it's taking me a bit longer to get it working. Thanks again for the responses ikegami!