I edited your title.
I've killed it with heavy gly but I'm sure there are better ways. Hopefully someone that knows for sure will chime in.
Long term I don't think it's going t be a problem like it has been in the past. I'm starting to see signs of Rose rosette disease on my place.
I used "Milestone" on a patch of smaller black locust. Sprayed it on topically and within weeks they were all dead. I believe this would also work on MFR. I really hate mutiflora rose as it has some of the nastiest thorns on it. It is really bad to cattle as it tears up their udders.
I wonder if fewer deer is a symptom of something else. I have the same problem, cut a tree and some MFR will sprout.
Hasn't seemed to deter the deer. But I did have to cut them a trail through one patch. Not a fun job!