I'd expect a bore worn bad enough that an oversize ring was being considered to have a pretty big ridge at the top of the cylinder. If new rings are installed, the ring's sharp, unworn leading edge will hit the ridge, often breaking the piston or ring.
Just one more reason not to cut corners. I'd suggest you look into some reading material
before going any further. The Vizard book on rebuilding the small block is often recommended even though it's pretty old.