I use the same thatch method with one change. I soak the towel in the water and wood glue mix. Then I squeeze the excess glue out. After I arrange the weave and let it dry, it goes rock hard. I found that every time I tried to add glue, I upset the weave. No matter what I did. I like your open frame for the towel to sit on. It looks like it gives you a natural bend between the rafters. I will have to give it a try.
Snitchy sends.