How would carbon affect compression? Unless it keeps the valves from closing all the way, carbon deposits increase the compression ratio. They don't decrease it.
I too used to clean the carbon off the top of the piston and maybe the inside of the head, but that carbon just decreases the size of the combustion chamber. The displacement of the piston remains the same, so the compression ratio is higher the greater the amount of deposits**.
Could cold rings and valves not seal well enough, so that the intake stroke didn't suck as much air in? I don't know. But that seems unrelated to compressoin.
**If I recall correctly, in mowers or cars, this can lead to detonation, running on, and knocking, because hot spots in the carbon ignite the gasoline vapor in addition to the spark plug doing so. But that's only after the engine has heated up. So carbon deposits can be bad, but unless they keep the valves from shutting, I don't think they can cause lack of compression.