Gary,
First of all, your questions are well founded, so please don't worry about being a pain. I usually scrape the horn to an even wall thickness so, when I use the tool to force it round, it is round inside and out. Also, I don't set the tool to make the horn perfectly round. I just adjust the thumb screws while measuring with a micrometer until the horn is close enough to "round" to fit or install a base plug. I do the same thing if I am working in the middle of a horn to measure for and fit a band.
Don't get me wrong here, I still boil / oil heat horns and use a sizer to make them round also, but, for me, this tool comes in handy for certain situations where I need to adjust the shape cold.
I made this thing one day when I had a horn that just would not stay very round. I had a devil of a time trying to get the base plug in because it kept wanting to jump out of the end of the horn. I made this tool, ran the thumb screws down on the high spots, forced the horn to a better round and easily installed the plug. If I wasn't such a poor horner to start with, perhaps I would not have needed the additional help. However, I almost never miss a chance to "over engineer" a problem.
dave C