I was reading that two layers of weed barrier in the bottom of a can/pot will keep mints from overrunning things. I would not suggest paper bags/newspaper/cardboard because I use livestock feed bags to line the bottom of my new raised beds to kill of the grass undermeath, but in a year or two they are decomposed. FYI feed bags are about 4-5 layers thick, so left whole that is 8-10 layers of thick paper.

Good luck
Bilie

I have the same problem. I don't know if this will work for the sunflowers, but I kept a lovely but manic iris in check by digging a trench around it (5 in deep) about 5 years ago. Now when it tries to grow across the trench which doesn't happen very often, I can see it in mid air and pull off the offending appendage. A bonus is that one of my little kitty cats likes to lie in the trench. Good luck, let us know if you find a way.