With the old rings in the bore, where the damage is, can you see light thru there and if so,
get a feeler gauge in there? (you shouldn't be able to get one in). A ring END GAP measurement
of the old rings be nice to know (measured about .5 - 1" down in the bore.
Ok, oversize piston and rings (.020" over) are available but ain't cheap(plus machine work):
https://www.partstree.com/models/20s232-1246-f1-briggs-stratton-horizontal-engine/camshaft-crankcase-cover-crankshaft-cylinder-lubrication-operator-s-manual-piston-rings-connecting-rod-warning-label-3/ For where you are now, re-boring / rebuild sounds a bit expensive.
Depending on much the cylinder leaks with new rings, right now is a crap
shoot.
Rings and gasket are not terribly expensive. If mine, I'd re-ring and seal it up..
You can up to 20% leak down and still have a good runner..
.
The head, if not warped, IF PARTED OUT, would go for about $50.00 alone, sooooo...