When I lived in coastal south Louisiana, where plants could and did take over areas, I would usually just whack the plant back severely with loppers or pruners. I would try to preserve a small section of it. During the winter is a good time to do this. Often if you cut the parts you don't want down to the soil level you can get control of it. I don't like to use herbicides or pesticides if I can avoid it. Maybe you could just whack it back. The clippings will make for good compost. I had some lantana that would take over my small pond, but I just cut it back and put the clippings on the compost pile. I had to prune (thoughtfully) things alot becoz I had a small yard, but I love to prune.

Yes! Whack it back as best you can! Clip clip clip down to the ground and then dig dig dig. See if you can get down to what I always refer to as "the root of all evil"! I would do it over time so as not to injure myself in the process. I would "not" try to save ANY of it because it will just take over again and you will NEVER be rid of it!

I had a friend who also gave me some calling it "tangerine plant" I knew about lemon balm and thought this was different. I just keep ripping it out again and again. it smells awesome though!

I had the same issue with oregano. The roots grew very deep, and it was a job and a half to dig it out from my flower bed.
Now I grow oregano in containers only, just like mint.