Carolyn, I handle it much like you...I keep a list, whether written or mental, on the regs and put them in when they walk in the door. That policy has a caveat: if they are consistently there to sing, I put them in the rotation...this is a reward for being a loyal regular. If they are the type to need a few drinks first and dont sing every rotation, I will not immediately add them to the rotation, I will wait for them to ask or hand in a slip.
I call the people who are there to sing and want to sing as much as possible "A-listers".
The downside to keeping a list is that if you depend on it too heavily, you are encouraging them to fall into the rut of mediocrity...but, chances are they are going to do that anyway.
Keep those lists, continue to treat your a-listers as such, but dont forget to encourage them to look at the books and try new songs now and again to help keep your show fresh for the non singers.