Lawn on a saltwater creek in Eastern NC - Bermuda / St Augustine

I've scoured the internet to try and find someone with a similar situation to this without much luck.

Situation:
My parents live on a saltwater creek in Morehead City, NC. Their lawn is probably close to .4 acres and is made up primarily of St. Augustine, some Centipede, and a new visitor near the creek named Bermuda.

Basically, my father brought in some soil to fill in some low places near the water which seems to have had some bermuda seed in it. What started as sharp, wiry grass near the water has turned into a lush, bermuda mini-lawn. Their yard floods roughly 1/3 the way up pretty frequently with the high tide and the whole yard will usually be under during a hurricane. The part that floods has had the st. augustine killed off and is now almost exclusively bermuda.

It's actually pretty remarkable. I knew bermuda was very drought/sunlight tolerant but had no idea it does so well under four-six inches of brackish, salt water.

My mom loves the bermuda, and would like to see it cover the entire yard. I told her it's an alpha grass and is waging some pretty solid war on the st. augustine and visa versa.

Question:
Can these two grasses coexist? What does a yard part bermuda/st. augustine end up like? The Bermuda has grown aggressively over the area that gets flooded. This year it's really filled in nicely, and I'm wondering if it'll continue to creep up even past where the water floods to or if the two grasses will just stalemate in the middle of the yard?

Also, Bermuda looks better cut <2 inches and their St. Augustine gets scalped pretty good at that low of a height (un-level yard due to lots of downed trees and whatnot). Should they mow the Bermuda at a lower level and the St. Augustine at a higher level? May be healthier for the grass, but in my mind their yard will be the equivalent of the bowl cut I had in middle school.

Any help or thoughts from someone with experience of this would be much appreciated.

PS: I've attached a Google-Earth image to show where the two grasses are meeting (well, not quite but you'll get the idea)