An actual reaming job with the cutting of metal would be an absolute last case option. If the frame was ever built up at some point then it must have been successfullly assembled with a seat post. It's far more likely that someone cinched down a too small post and egg shaped the upper part where the relief cut is but the rest is OK. What you can do is figure out where the tight places are by offering up the end of the post to the frame and looking carefully. With those spots marked on a wrap of masking tape you put around the top of the tube use a one or two size smaller seat post or a close fitting but slightly loose pipe as a try tool to open up the clamping area back to round. To get good leverage but ensure proper support you want to insert it so the end goes in only about 1/2 to 3/4 inch past the end of the relief slot. Then pry the post to one side towards the tight spots as marked on the masking tape. The idea is to gently bend those areas back out to round. Obviously start with firm but limited pressure and use the proper size of post to check your progress often. If the steel flexes and springs back then increase the amount of pressure you're using until it bends back out to round. When you can insert the post to the end of the clamping slot with the usual effort then likely you'll find that the post slips in all the way without undue force being needed. Don't worry about going very slightly too far with this process. The steel will happily reform to a proper fit the first time you clamp the correct size post back in.
And keep in mind that a seat post is seldom a drop in situation. Many a bike has just enough distortion in the frame tubes that some slight twisting action is typically needed. But of course if your post goes to the end of the reformed and slightly enlarged clamping area and then needs more than a light but firm push or just plain jams again then perhaps your post is one size too big for the frame.