Wow, next they'll be telling you to get a borescope!
Those compression numbers from your first legitimate test are low. They are lower than low.
You said there is a lot of carbon in the engine. Last year Hot Rod magazine in one of their "we fix a problem car" articles worked on a mustang and it had low compression in some holes. The mechanic said lets take it out and "blow the carbon out." I always thought that was just a myth. He told the writer that sometimes engines get carbon deposits holding the valve a little open and losing compression.
Go out and get the car warmed up[, do a bunch of hard acceleration runs and some high speed runs. That may help. Get back home and aim the exhaust system away from buildings, people, etc. Remove air filter and with engine running about 2500rpm, trickle some water into one side of the carb. You should get a blast of white steam, maybe carrying with it little chunks of carbon. It's pretty dramatic and will stain a wall or fence. Repeat for the other side. Take it out and run it back up to operating temp and do it again. This may help.
It sure sounds to me like rings aren't working. Try to seat the rings with some sharp acceleration blasts followed by letting the engine pull the car down to speed with throttle closed.
Leakdown tests can tell you the condition of things. If you pressurize a cylinder and air leaks out past the piston the next step is surgery.
The initial and second set of compression results were done with a rental gauge with unknown history from a local auto parts store. The results were questionable. The latest ones were done with the new gauge and were in within spec of > or = 110.
Can rings become unseated? If so how and why?
If I do the leakdown on a warm engine and get good results vs bad results on a cold engine what would that mean?