A authorized Biggs and Stratton repair place will not re-ring it, or rebuild it with oversize piston/rings, they would either shortblock it or repower it.
Have you tried the valve cover test. Remove both valve covers and run on low to medium speed out in the yard.
On a normal engine, the heads will just dribble some oil, if the head gasket is blown, it will spray compression/oil everywhere.
Then go to store and get a head gasket or two for $8 each, and replace.