Could I measure the surface temperature of the copper lines that enter and leave the unit in the house? Would that be a different general indication than the air temperature readings through the pinholes?
I don't think so; the gas going in only cools when it expands in the cooling coil, and then picks up heat in the coil itself, cooling the air. There may be some, or almost no difference in the gas temperature before and after it goes into the coil. The general test a repairman would look at when checking the gas would be the pressure difference between the two sides. For that, you need the right tools and gauges and the specs for the unit. Even then, this would only show the compressor was not the problem---you could still not be getting proper cooling due to other problems.
What you really need to know is what is happening as the air passes over the cooling coil itself, and the test for that is the temperature drop of the air before and after it passes over the coil.