I think at this point, herbicides are your friend.
If you clear all of it, or even just a portion, I believe it will be much less work to control it in the future by spraying.
Also, if you are hand-cutting through there, you may benefit by creating some access paths now and starting herbicide treatments on your big stuff. For example, I can easily kill my honey locust trees up to 20' tall when the basal bark is still smooth. Once it gets rough, then I have a lot more work! Sometimes, I spray the easy stuff that I can access from my "paths", and then expand my paths the next year.
Frequently, I just mix up a dose for my 2-gallon sprayer when I know I am going to finish my chores before dark. I always grab my respirator mask and then spray until empty. Then I throw those clothes in the laundry and take a shower. You will always get a little "drift" on you and your clothes. As you start spraying more as a property owner, your safety protocols have to get a little more stringent!
Go back out a couple of weeks later and spray the stuff you missed. I usually go when the effects of my previous treatment are obvious so I don't double spray.
Sometimes the next treatment is with a different herbicide. For example, your best treatment for locust trees may be different than the best for multiflora rose.
Finally, the more you beat back that stuff when it is only 2-3' tall, the more likely you are to get patches of grass established the will inhibit some of your undesirable plants from flourishing.
