I gather if you pull the fill cap on the valve cover, you'll get lots of oil "vapor" coming out?
What your describing is piston ring blow by, IE the rings are worn out-allowing combustion gases
to push into the crankcase.
As long as the cylinders are not scored up, no MAJOR wear to them, you can hone the cylinders and simply re-ring the pistons / engine...
My 18 HP Brigg's (from my Toro zero turn). Had to replace the piston, rings and head
as a valve seat let loose... Cylinder was fine, just a hone for the new rings to seat..
That was 5 years ago, doesn't burn a drop of oil (nor leak):