Its only my opinion, but I wouldn't put any additive in the oil which would prevent the rings bedding in. If the rings don't bed in properly they "glaze" the bores, it will always be tight and will always use oil.
The sensible thing to do for a long term solution in my view is take the head and barrel off and check the ring gaps in the bores. Maybe the dude who rebuilt it forgot to "gap" the rings and when it heats up, it tightens.
If you haven't done this before, you take the rings off the piston and push them one at a time into their respective bore and push it down an inch or so with the piston to set the ring level in the bore, then check the end gap with a feeler gauge. You should have a gap of around 13 thou for the compression rings and 11 thou for the oil scraper.
If they are any tighter than that check the piston clearance you should have about 4 thou piston to bore clearance - if you have, its bored to the right size, so then you can set the ring gaps as above, you do this carefully with a smooth file on the end of the rings while held gently in the hand.
If there is too little piston bore clearance you will need to take the pistons and barrel to a re-borer and have them honed to size.
While its apart, look for seize marks on the pistons, if there aren't any, its not the pistons seizing - but it could still be the rings.
If you've never done anything like that before, I would recommend you get experienced assistance as the rings can break very easily.
If you already knew all that sorry this has turned into another epic.. I'm going for a lager.