Sadly I think you've answered your own question and the only real solution is a one user/one group scenario. I bow to others' superior knowledge though before betting my life on it.
The only thing I can think of off the top of my head where, in general, user permissions are already pre-defined is that of the MyTiki features. Of those, probably "tasks" is the only one that would even slightly meet your requirements in that the professor/s could "send" tasks to individual students but this is a very unattractive solution.
I know some of the moderators (for want of a better term) have some experience at using Tiki in an educational environment, so they might be able to provide better solutions.
Failing that, try the open source project Moodle (not that I want you to stop using Tiki because I think it's awesome!)