I agree, you are not losing air according to the symptoms.
Just for some history, I replaced a faulty above ground check valve with a new check valve.
What caused you to think that old check valve was faulty? It sure looks like the new on is faulty.
You probably have more than one problem not counting described leaks that presumably total well under 1/2 gallon per minute. If everything else was OK, there would be no job for your above-ground check valve to do.
Regarding a possible hole/leak in the drop pipe or pitless as Letsrunum suggests, you could pull the well cap and listen for running water. That could identify a problem, but it would not let you hear/see a problem below the water level. You could light up the inside of the casing, especially around the pitless adapter (about 3 or 4 feet below ground level), and look for a flow. For a light you could reflect the bright sun with a mirror, or use a bright flashlight. I would hope you would not contaminate the well while troubleshooting.
You might even be able to hear something with the well cap on and your ear against the well cap. I don't know. I have no experience with that.
Letsrunum's suspicion makes good sense, and if the problem is down the well, you should have a well specialist fix it.