I can think of two ways to do it with out the carpet being under it.
If you like the like it has right now. Cut out a circle smaller than the base and install a piece of plywood slightly thicker than the carpet and bolt it down.
If you like the look where the carpet goes under the molding.
Cut a hole slightly smaller than the base, remove another inch of underlay.
Slide in half circles of 1/4 plywood to replicate the tack strips and work the post thru the hole and bolt it down and then tuck the carpet down.
Thanks for the great tips Neal but I couldn't get comfortable with the idea of cutting the carpet so I got a side mount post and screwed it to the knee wall. I originally thought I would need the extra support of having one of the posts screw to the floor but after having all four side mount posts installed it feels very sturdy.