Andrew R Stewart 

Yes, terms matter and the "seat post" is really the frame's "seat tube".

I see chips on the seat lug's ears right where one might place the tip od a screwdriver to try to pry out/bigger the seat post fit. IME this suggests a too small post was once used and the lug closed up some and someone tried to "fix" it. Or perhaps the post had just started to seize in the seat tube and the prying was an attempt to free up the post.

What most have said is good advice. The safest solution with the least "non reversable" result is to use a small enough post. Next up is doing mechanical working (blacksmithy with slightly small posts or pipes) on the lug area to open up the fit at that point. Running a hone down the seat tube top portion to remove burrs is a good idea regardless of what path is taken, honing doesn't remove hardly any bulk but is great at small high points. Last would be running a reamer, which is designed to remove bulk, in the tube and a honing follow up.

But when reaming it can be tricky to track what is actually being removed, one wants to avoid tube wall removal below the lug's lower edge (as that's only the tube wall below). Having said that often the critical area of heat deformation is right where the two different wall thicknesses meet (wall 1 being the tube and above that wall 2 is the lug/tube combo with braze filler between). I have seen more than a few frames where the seat tube was heat bulged significantly just below the lug, How far the resulting "correction" can be done can be limited by the frame's condition.

A commit on the OP's assumptions- One metaphor I like to use in talking about post fit is one of choosing a pair of shoes. One picks a "size" that fits the feet, regardless of what a shoe sales person thinks they have measured (such a word, filled with so much presumed fact) you feet as. Or at least we hope the actual fit is the final guidline and not the suggestion of having foot surgery to have your foot be able to fit in a shoe. Of course there are situations where foot surgery is the right choice (I have two TI plates in my toes...) but I think we can agree that we should do our homework before cutting skin.

I also question the OP's measuring methods, tools, results. There have been a few seat post fitting threads here recently and my advice here is the same as with the others. The only measurement that really counts is how the post fits and is secured. Very small amounts of diameter "drift" result in 22/7 (3.1415) huge amounts of circumference increase. And the sear lug has to clamp around the post's circumference. Given the OP's challenges with basic tool/measuring challenges I suggest they get someone who is more experienced to help out. Perhaps even show the OP some tool tips. Andy