I have several steel culverts from with diameters of 3.5' to 5'. See photo.
My plan #1 was to put the largest one in dig it out, put in next, dig it out etc....and then put gravel in the bottom.
Don,
I sure don't know anything about Texas stone. Up here we would call the aggregate in your picture... limestone. Our gravel comes from rivers of past centuries and present rivers. It is irregular in shape but somewhat round in shape.
What it is called doesn't matter. The difference is that gravel does not pack together under pressure so it allows the water to continue to come up into your round culverts from underneath. Limestone or sharp cornered crushed stone packs together and forms somewhat of a block.
That may be your intention?
Ron