Here is some more to think about,

Before changing the thermostat, drill a 1/8" hole in the edge of it to let air out of the head as you fill the coolant system. You can also force the stat open and slip a aspirin in the opening, as coolant enters and air exits, the aspirin will melt shutting the t-stat.

Forget the vacuum gauge, you can never get a steady reading while driving. Its doing what it should be doing. As for being low, who knows, it might be right for your engine, not all are the same, age, wear and tear all make a difference. Driving with a vacuum gauge is for fuel milage, try to keep it as high as possible and you will get the best fuel milage. That will mean a very tender foot on the accelerator.

Advancing the timing will bring up the vacuum at idle, its a good way to adjust the timing if you don't have a light. The idle speed will also increase as the timing is advanced, so back it off as you advance the timing to keep the mechanical advance weights in a closed position. As the engine speed increases, the timing should also advance from the mechanical weights being thrown outwards. You can check this with a timing light, slowly increase the throttle opening and the timing should slowly advance. In 1937 the distributor is designed with 46 degrees total advance @ 3500 rpm with 17 more degrees of vacuum advance. Our modern day fuels are much better then when the truck was being used, and your compression is way low compared to a modern engine, so more timing will have no damaging effects on the engine. If it helps great, if not return it back to where you started.

You carb is not running rich or it would climb hills. You have something wrong in the carb that is not letting the power circuit kick in. Engines require more fuel under a load such as climbing hills, so the carb is designed to increase the air to fuel ratio as the throttle is opened farther and farther. Get a shop manual and read up on the power circuit of the carb you are using, then pull yours apart and fix the problem! Reading my '37 manual, the original carburetors have a moving metering rod which adds fuel the higher its pulled out of the jet. Its a stepped rod with the power mode at the tip. If yours is not working or is adjusted wrong, it will never get to the power circuit thus causing your hill climbing problems.

Idle adjustments only effect idle. Once the throttle is open, it bypasses the idle circuit.

Vacuum advance will also not effect the power circuit since the vacuum drops to zero when the engine is accelerating. Vacuum advance is good for fuel milage, it pulls in a bunch more timing at light throttle or cruise when there is little or no load on the engine. As the load increases, the vacuum drops and the timing retards back to the original setting. Just make sure its working, theres no vacuum leak, and your timing is set a few higher then stock.

Joe