Mowing definitely helps. I mow all the time.

But it has made an enormous difference.
If you're dealing with the invasive sumac, you have to pull out and/or cut the roots. I had (have) a horrible time with sumac and found that a combination of pulling roots and squirting with Roundup formulas did the trick. In some areas. I still have several more areas to go.
I also have some invasive bushes --- really bad ones. Roundup squashes them, as well.
I get dry roundup at a local feedstore and, for the invasives, mix it MUCH more strongly. I also use it on multiflora, with success. :yeeha: It has sucessfully cleared two entire hillsides of my invasive bushes and tons of sumac.
Mowing and keeping after it, though, is the most important thing to do. I don't even let the sumac, multiflora or bushes get going in the areas I've cleared and am hoping to get another area cleared of them by next year. :yeeha:
You have my sympathies. I never knew how awful invasives were til i got this place. :no: