Been a long time, and it may have been on a case by case basis but at Stones River I would encounter the occasional full auto.
Cheatham county had a pretty much open to anything outdoor range
Owl Hollow in Spring Hill MIGHT (if they are even still there)
There are a couple indoor ranges across that state that rent class 3 stuff but again it’s been a long time so I don’t remember them off the top of my head.
Any of the above may be out of date but might give you a starting point.