Myke I think you can do anything that's provided, so if you just want a CBJ, most will be fine with that. I'm not sure they'll offer much of a discount, though. Maybe from 160 for FS to 140 for a CBJ, for example. Its more about their time than the actual service.
Bigger question would be if you can do a covered CIM. Some may not allow it as they fear leakage.
Never hurts to ask.