I think vinnycom makes some good points.
Extra carbon in the head will actually increase your compression ratio a bit, theoretically increasing power by a touch
You don't need a spring compressor to check valve clearances. Just remove that little side cover (assuming it's like my engine), as well as the spark plug, and follow instructions for checking clearance, comparing the results vs the specs.
Yes, that sort of compression tester will do what you want. Compression tests can be a bit tricky to interpret, however. There is an automatic compression-release on most engines, which will give "artificially-low" results. It props one valve open just slightly during the compression stroke at low RPMs (like when starting it), to make it easier to pull. This bleeds off some pressure. The amount of compression reduction is based, in part, on the current valve clearances.
If you *really* want a reading subject, you could look into leakdown testing. Leakdown test are done with the engine not spinning, so it's kind of a more controlled test. You then add your own controlled air pressure source *to* the cylinder, then you listen for where the air is leaking out of the engine.
Air is leaking out the crankcase, through the oil filler tube? Leaking piston rings. It's coming from the intake? Leaking intake valve. It's coming out the exhaust? Leaking exhaust valve. Coming from around the head? Leaking head gasket.
To do a leakdown test, you might position the piston a little past top-dead-center (like when checking valve clearances), so that both valves are fully closed. This is unlike when using a compression tester, which, again, has the valve pop open slightly during the test, due to the compression release while the engine is turning. With the engine in this "tight" position, you can better evaluate what's sealed, and what isn't.
Some info here about how to make your own, simple leakdown tester, if you were really inclined:
https://www.mytractorforum.com/44-s.../44-small-engines-repair/1279105-low-compression-lawn-mowers-advice-needed.html
Or, frankly, the proper fittings, along with the compression tester adapters, might do it.
After reading about the DIY leakdown tester, I may try making my own, just to have it available. Ripping a spark plug apart sounds like a bit of a pain. But I have a welder, so I could attach a steel air fitting to the core of the plug. But if you had a compression tester, that gives you an interface to the spark plug hole, and you might just need to come with a way to connect your air compressor to that.
I haven't done a leakdown test, but I'd be leery of using much pressure for a test, at least initially. I'd start with maybe 5-10 psi, 20 tops. With a 3.3" bore, 20 psi is putting 170 lbs of force onto the piston. I think you don't want the piston exactly at top-dead-center. Which means that your air pressure is trying to make the engine spin, so the piston can go to the bottom. So don't touch anything on the engine or machine that could potentially turn, while pressuring the engine. Safety first! Locking the flywheel in-place (maybe with a ratchet strap wrapped around?) might be good for safety and consistency.