IF you could completely kill ALL bermuda from your yard… then I would go for it, replace with a carpet grass as I assume you are in a higher rainfall area (more than 30"). It does great in shade as long as it is not complete shade all day (either dappled shade, or morning or afternoon sun are ideal, low maintenance spots for carpet grass to grow down here, full sun needs supplemental water during our droughts). Our yard at the farm has carpet grass growing under two 100ish year old post oaks to about 20’ past their drip line with no irrigation (they love the dappled shade), just natural rainfall of ~30"/year, and has been that way for 30+ years since mom and dad bought the place; sailed through the drought of 2011-2015. The carpet grass will spread during wet years, and retreat to the normal dripline +20’ during dry years. It’s aggressive enough to drown out other grasses / weeds, but not as agressive as bermuda in sucking up moisture / nutrients from your trees, and MUCH EASIER to either trim or spray back (once a year usually will keep it in it’s place). I don’t know where you are in 8A, but i know that 8 is it’s northern limits, so you will want to check and make sure from a local source!