The original bore diameter doesn't matter. Measure what you have now and then search out new rings or a new piston to fit it.
The better way is to buy a piston / rings and then have the cylinder slightly bored so it's nice and straight fits that piston. Use the services of the bike mechanic or machinist to help measure everything and to pick the parts before you buy anything.. He can also examine the engine's bearings and stuff and maybe save you some grief later.
While you're in there, measure the stroke yourself. Remove the head and fasten the cylinder back down snug. Use the mark on the flywheel to bring the piston to TDC. Measure how far the piston fell after turning the flywheel 180 degrees to BDC. Take your time and you can get really close with just a straight thin measuring tool (or even with a cheap caliper).
Then find a kit built for the same or nearly the same stroke. Minor differences can be corrected with things like thicker/thinner base and head gaskets.
If that bolt pattern exactly matches Puch, it's a big clue as to where to look first..
Isolate the rings as the source of the low compression. Squirt some heavish motor oil around the piston crown and see if compression rises.
_it just turns into a slug when it hits the slightest incline_
This could be normal.. all vehicles are gonna go slower up a hill than on the flats. Gross weight matters when climbing hills.. A stock 2-stroke moped is expected to eventually slow to pedaling-speeds on anything like a long, genuine hill.
But if it's unusually bad, the problem could involve carburation or exhaust or other things. Give it a tune-up.