From looking at the documentation for Bitnet (which seems a bit old, using RPC version 1.0, though I may not have found the right one), I'm not sure it supports SSL, or the verifymessage command. Have you tried using "http://" and port 80 to see if it works without SSL?
Well I'm trying to do this all online, not running bitcoind on my computer, and I think that's where the problem is. I've also tried it without bitnet.
If I have to do it running bitcoind on my computer, then I'll have to approach things differently (which is fine).