I would try a different pressure gauge before I spent any money on other solutions. Keep it inside at a constant temperature before using it. It's a long shot, but this would eliminate one potential source of the puzzle. And - don't just assume the pressure is decreasing because of a temperature change. You have a leak in all four tires, or someone is letting some air out when you are looking elsewhere. The laws of physics reign supreme - matter (such as the air in your tires) can neither be created nor destroyed.. Note - the lower the tire pressure, the slower the leak-down rate.30 degree F swings should give about 6% change (approx 30/500) in pressure. So at 40 psig (55 psia), that is only a 3 psi swing.
N2 obeys the ideal gas law just as dutifully as the other gases in air do. The difference is that air pumped in from an air compressor will typically have some moisture in it. The temperature-variable evaporation/condensation of that moisture between liquid water and gaseous water vapor is the thing that affects pressure. N2 in tires is typically dried (all H2O removed) as part of the procedure that extracts it from the air. Dry air would be just as good at resisting thermal variability.
But (as I read it) the main surpising point of the OP is that she loses pressure when temp goes down 30 degrees. And she loses pressure when temp goes up 30 degrees. And the other very weird thing is that it is the same on all 4 tires, making it less likely to be a bad valve, bead seal, puncture, etc.
So I'm really stumped on this one. Hope the info I provided above is helpful.
It is almost beyond any reasonable explanation why all four tires would leak down evenly unless it was maliciously caused, unless all four have a similar nail puncture or say, some cord or wire trapped in each tire bead. Once I rode over a board with a very small tack in it. I found small, similar punctures in two of four tires. Maybe a soap solution sprayed on the tires will find the leaks. Maybe someone was up to some mischief with a hypodermic needle?
Submerging one tire in a tub of water will find the smallest leak. Finding one leak might help you find the others.