Rzimmerman, no, I haven't tried LEDs on my seagrasses. Mostly because I'm cheap, and I already had a 400 watt metal halide fixture to use. Other factors include the 30" depth of my tank, and the overwhelming selection of good and bad LED fixtures.
I do think they should work well, if you get an appropriate one.
Sorry to hear you had bad luck with thalassia. I too had a struggle with cyanobacteria. Turtle grass tends to need a more established sand bed. Shoal grass and manatee grass are both pioneering species, and do better in newer sand beds. In my tank, as in nature, the turtle grass gradually overtook the manatee and shoal grasses. I have since removed it, preferring the shoal and manatee grasses.
Seagrasses need lighting every bit as bright as reef tanks, if not brighter. And because they are higher plants, they have actual roots that seek nutrients in the sand. If I were starting a new tank for thalassia, I would put about an inch of dirt out of my yard on the bottom, and cover that with another five or six inches of sugar sized calcium carbonate sand. I also recommend Florida Pets' live mud and Gulf Coast Ecosystems' live sand.
Good luck!