Try these programs. PeerGuardian 2 and IP Traffic Monitor. Ip Traffic Monitor can help show what is happening and who is connecting. Peerguardian will block spambots and robots and not even let them get to your server let alone your board. Do you have robot.txt as many robots, etc look for that file?
I would sign in as a new user and see if it actually sending a registarion reply request. If not, that may be your problem. If it is working I would agree they would have to be humans. Are you getting bounced emails sent to you because of failed email addresses sent because of invalid addresses?
Sounds like you have enough on your plate to be going to phpbb3. I tried it and it is a bear. Completely different setup which is troublesome sometimes and the admin and formun setup is completely different. The permissions setup isn't fun. There is a learning curve. I am not even sure if they have an authorized upgrade conversion yet.