In reply to original poster:
A lathe is a very handy tool, but you need a 4-jaw to get the cylinder to run true. Then it is easy to adjust the combustion chamber to the piston dome and get the right squish of 0.5-0.8mm. Most chain saw engines have a larger squish to steer clear of mechanical interference.
Remember that lowering the cylinder also means you have to raise the exhaust port. Lowering also means that transfer is reduced, so the engine becomes more sensitive to exhaust system. Using canisters instead of the garbage side dump systems (which BTW can be quite sophisticated) would call for some extra exhaust port raising. The increased blowdown is a free bonus for better power, again IF the muffler takes advantage of that.
Regarding high CR:
It is not always advantageous. Better gas flow is more important for mean effective combustion pressure. Raising the CR just raises the power by some 2 - 5% whilst very much shortening engine reliability. Improving the engine basics without raising CR can easily bring 25% extra power without reduction in engine reliability.
The sad thing is, that rubbish in, is rubbish out. Starting out with a bad engine is not the best idea, and probably will cost quite a lot more than investing in a better engine right away.