the fact that you want it to interface with your current user system, makes the problem quite difficult. you would most likely have a headache trying to get your current user system to work with the forum software's system.
it is my assumption that some of the better (and free) forum packages like invision board, are modular enough so that you can simply disable whatever sections / features you want. you don't have to have mods, for example, it's an option, and simply having it be an option, might not necessarily slow things down.
obviously, the best solution, if you're even considering it, which shows that you must have the time, is to code your own. depending on your skill level, it can be a challenge (it was for me), but it's also rewarding. the other downside is that you can't visit said forum's tech support forum for help when something is buggered up 🙂
i don't know of any barebones forums. there are some that look quite barren (phorum, for example), but i wouldn't expect to find a forum package that doesn't have a user system, for example.