RE the St Augustine invasion. This is the first year of 5 I've experienced it in my backyard lawn. I have Bermuda and overseed with Winter Rye... so the St. A has "never touched my lips". I'm pulling it out as it appears. Birds are amazing transfer agents. :(
Chris, I did the same as you re layering over Bermuda. Five years ago in heat of summer I pour Distilled Vinegar over a specific area and later layered with cardboard. RE using vinegar, you need to let the heat and direct sunlight hit the plants in order to kill or arrest it's growth. It worked.
However, I do experience Bermuda creeping under the concrete and brick separators between grass and beds. I dig up the rhizomes immediately.