i solved this issue on day one. they injected hot gas into the football right before the pressure was measured. pressure was fine with the hot gas, but once the gas reached ambient temperature the pressure was lower. Using the ideal gas law I calculated the gas would need to be 30 C (about 55 F) hotter than ambient. Completely feasible.
I'm willing to bet that you used 2 PSI in your calculations as that is what was initially leaked as the pressure difference for all of the footballs. There have been further leaks saying that only the intercepted ball, the one in possession of the Colts, was 2 PSI low. The rest were supposedly under 1 PSI low.
Based on the information from Billichick, it's likely that at least one of the footballs, if not more, were roughed up (which is what they do the prepare the footballs) just before the testing. This also could account for the internal temperature of the air being higher than ambient.
For those asking the question about whether the league should understand what happens to footballs, the answer is that Yes they should. But No, they have never seen the need to delve this deeply into it before. The Refs don't even put the football pressure readings on paper when they test them, assuming that they are actually doing their job and using gauges. You would think that in this day and age that they would test each football, record the readings, and stamp it with a random bar-code.
They could probably use a temperature gun to measure the ball temperature prior to taking the pressure reading. Or, for that matter, the pressure gauge should have a temperature gauge built in. Enter this information into an app along with game time weather and they could use it to set the football pressure for game conditions.
There... an new App for the Microsoft Surface... Football Pressure Calibrator for Weather Conditions (FPCWC)....
PS: I would have typed that this would be a new app for the iPad, but the NFL has a marketing deal with Microsoft.