I've always relieved the hole in the hollow mill just back from the cutting teeth.
On a large bit, a boring bar works OK. On a small hollow mill I just drill back down from the top end and stop short of
coming out the cutting end.
Both to leave a small pilot shoulder to guide the hollow mill, but relieved back up inside so there's no interference betw the mill cutter and the post you are cutting. It doesn't need a lot of clearance.
Otherwise the post you are cutting is the same dia as the pilot/guide hole in the mill,,,a force fit for the entire length.
The newly cut post, say 1/8d is being forced into an 1/8"d hole. The post strips off matl/galls as it is forced deeper in., ends up smaller in dia than supposed to be, or misshaped,or sometimes broken off up inside the hollow mill
Anywy, that's the way I've done it as I had problems with a simple hollow mill cutting a simple post.
A short post can be cut with the same dia pilot hole in the cutter I found, Say it's height and dia being about the same. But after that, I need to have some clearance for the post to turn in there.
See if the drill you used to drill the hole in the hollow mil will still enter than hole,,or perhaps the hole is diminished in dia now with material from galling and sticking the the sides.