The very first week in Sept will be very busy in the MBNF, lots of campers for Labor day weekend. Some years the elk just don't talk then but last year they were vocal . You'll likely see more hunters than elk that 1str week but they will be close to the roads.

Last week in Sept lots of folks show up to set camps for deer season and will bow hunt a few days for elk and deer, more folks on the mountains then too.
Plan for the most week days you can hunt for your dates and you'll have less resident pressure.

3 rd week usually has elk talking, but again you never know.