Air leaking past piston rings?

The rings are designed to be exactly round at exactly one diameter. You can gap them to whatever you want, and in the hole it was designed for it will still be round.
The top ring has little to do with oil-burning, that is the job of the oil rings to prevent.
If you take a too-big ring, one that was designed for a bigger hole than the one you are putting it into, it will want to touch the cylinder walls in about 2 or 3 places. Just put one in a hole sometime,square it up, and make a cardboard plug a little smaller than the hole and drop it onto the ring. Weight it down lightly so it sits on the ring flat. Then shine a light up the hole from the bottom. Shazzam!
Now as the ring wears at the contact points, it will soon expand as it wears the high points off.Eventually it might wear to fit the hole, but in the meantime hot exhaust gasses are being being forced into the crankcase, and in the end it will have a huge end gap, and lotsa leakdown, which is why I recommended the LD test; to see if you even had an engine left.