Your garden looks lush! It is always better to have more good plants than weedy invasives!
I have the same wild petunia growing in what we call our meadow, but it is in dappled shade all day under old-growth trees. It is a volunteer here. Your garden looks like full sun, you said it is the west side, am I right or is it less than 8 hours, some shade maybe? If I could move some of my petunias to a more sunny area that would help fill in areas rather than spending money on plants that might not agree with my soil pH, etc.