Would it be possible to make the carbon tube more rounded on the bottom same as the top? Bring it down in overall diameter a little?
Certainly. The current shape was really driven by only three factors, and they are flexible:
1. I kept the bottom relatively flat, so that the handle attachment could be a simple "screwed plate" design similar to a typical handle. But this really applies only in the handle area. An if you wanted to go with a mortised handle, as you have done before, then the bottom could certainly be more rounded.
2. I didn't show pics, but there is an intermediate step where I clamp it from top and bottom to push a Delrin "dummy" piece down from the top to force the carbon fiber down into the track recess. I learned from the tube on my hybrid that clamping from above will tend to produce a slight flat spot on the bottom of a fully rounded shape. But the flat area is only 1/4" to 3/8" wide, so the bottom could certainly be more rounded then I made it in this case.
3. Squarish sides and bottom make it a little easier to hold the wax in a vise repeatably when cutting the wax "ingot" to the final shape. But again, only a small flat spot is really required.
I did calculations before I started to make sure that this gun would balance well with a 5/16" shaft, 10" of overhang, and a full 1/8" wall thickness. I think it would certainly be possible to make the tube a little smaller, especially if intended primarily for a 9/32" shaft. And 3/32" would probably be plenty of wall thickness.