I have two patches of wild ageratum, one of which I want to eliminate because it has spread too much and is in the way of a shrub that I recently planted. I would want to mulch the area around the shrub and sow grass seed over the rest (it's adjacent to our lawn). The area is about 8'x10'.

I imagine if I just pull the ageratum and overseed with grass seed the ageratum will grow back from roots and older seeds. I don't mind a few sprouts here and there (our "lawn" is a mixture of violets, clover, and unidentifed weeds along with turf grass anyway and I'm ok with that as long as it stays reasonably green), but I don't want the ageratum outcompeting the turf completely.

So I'm wondering what else I need to do. Solarize? Put on a thick mulch over the winter? I don't want to use chemicals. Thanks in advance.