If I were to organize this it'd be something in the lines of:
Create a Thread, possibly make it official by asking a mod, in General Discussion and/or Tutorial (if they don't want to let us renew the Mentor Program board);
This Thread is used to list all of the Mentors in the OP, with their Time Zone and, if needed, some notes about them;
In this Thread, wannabe apprentices can see who they'd want as mentor and PM them;
After that, everything is no more dependent on the Mentor Program itself, but it's just two users in which one is explaining the other stuff via PM, chat or whatever.