I have fished for those grass carp several times in Brays. The ones that are not mullet are 95% grass carp - which means they are primarily vegetarian and they can be extremely wary. They dont spook and disappear as they are very used to people there, but if you approach too closely, or you catch one then they just seem to slink off and sit in the deep channel in the middle. They only thing I have got them to eat are surface flies that consist of spun brown deer hair, trimmed underneath to look like a general brown seed, beetle immitation (or something worse..this is the bayou afterall) - and the trick seems to be to either present it upstream and cast a couple of feet in front of their mouth and let it drift back, or a downstream presentation far enough ahead of the fish that they dont see you. I have given up on nymphs or streamers as you just end up in the algae and being grass carp they are highly unlikely to chase a streamer. iFly sells the fly, but sometimes they hide it in the draw. Hammer makes a good one too.
Yeah you are right about the banks being uncomfortable - but its probably better than wading all day in that water. Interestingly I took a trout fishing friend there a year or two back and he just waded right out into it in shorts and came back with all the flesh still on his legs..I was shocked as I thought it would just be bones left.
I have found that the section along Braeswood and particularly around the intersection of Stella Link and Braeswood is a good place to start.
You need good light to help spot the carp - the gold is a giveaway. And there are a lot of big fish in there. Some of them fight really hard, others just seem to roll over and flop around a bit.
Give me a shout on 832 444 4206 if you want to go another time