Here's my thoughts on your project.
In what county is the site? .. Clay 'bathtubs' sounds pretty off the mainstream. How would they be fired to make them water resistant? Unless this is FAR East TX, the rest of TX never made enough clay goods for a tea cup.
By definition a 'mound' is purely an accumulation of fire rocks used in cooking. It's a certainty that the people were grouped around these areas, in cooler WX just for the warmth and also when it was time to get to the food. So there HAS to be some strong evidence of their presence ( Bones, Manos, basic flint cooking tools etc )
I can think of three good reasons why you have not made any finds...
There ARE middens ( mounds) with ZERO artifacts in the matrix...Concentrate exclusively UNDER the fire rock, a narrow trench into & away from an obvious mound would be best for understanding future mounds.
You are far enough East in TX that they are NOT true fire rock middens but rather ceremonial mounds which has no guarantee of having anything in them except a lot of construction sweat. Hit the books for Caddoan culture mounds.
Those are not run of the mill mounds then, certainly not middens. I have one 9 inch blade, very thin found in Hays county. Closest ID is a Caddoan Blade.
Couple experts agree it must be ceremonial only as it's too well made and fragile to be utilitarian. Overall blade design looks Covington teardrop.
My thought is that there are surely " camps " on the property in the vicinity of each mound but level with the present surface...tough to locate but would
be very interesting to identify exactly what type & age points of the people that might be responsible for the mounds.
A pic or two would be interesting to our readers,,,if your in the mood