Yes, you can change the piston rings whilst doing the top overhaul. Remove the oil pan, remove the conrod end caps and push out the piston with the head-off. While at it, replace the conrod bearing as well.
However, if the cylinder wall is scratched, its better to drop the entire block to bore/hone it. Strongly recommended to hone/polish the cylinder wall if possible as you do not need to install oversized pistons (more costly). Not many workshop will replace the piston rings while doing the top overhaul though.
On another note, compression might still be good with fried piston rings as only the oil ring could be fried while the compression ring could still be good (which could explain why your engine still has power).
Just my 2cents...