For the 69 300 that apparently does not have autotemp 1 (you are very lucky because those systems usually can not be fixed) there could be an issue with the control switch behind the pushbuttons. I would think that would be a good place to start with a new or nos one. A competent technician should not have much problem replacing the unit. It consists of removing an ash tray, the radio and then reaching up in the dash area and removing and replacing the control switch.
Your 72 Imperial is Auto Temp II which is repairable. However, before launching into replacing the control box under the hood or the amplifier above the glove box, I would suggest you actually do replace the check valves in the system, as if any one of those fails, the system will shut down. They cost several $$ each and are just small plastic devices with nipples on each end. In the hose bundle just under the dash panel, you will find most of them. Just remove and replace each one since after all these years they are all bad or soon will be. Then retry to operate the system. You can do this yourself.
If your control unit under the hood has a red round body on it (black on top) with a bunch of hoses connected to it, I would suggest you replace it anyway even if it does work because it won't be long before the housing will crack and leak coolant and you might miss the car overheating and ruin the engine. The replacement units are fairly expensive but worth it because they have aluminum bodies instead of the red plastic ones from the factory that are junk. The aluminum housings will not crack.
Performance Analysis Company makes them with the aluminum housing that will not crack and they will even provide support to customers who need assistance in getting their systems to work. Also I would recommend buying a new amplifier at the same time. Here is their contact information:
Performance Analysis Co.
They can also likely supply the check valves for your system or suggest where you can acquire them. They are very helpful with any issues you encounter with your a/c system.
A couple other thoughts - I personally would remain using the R12 refrigerant as it seems the older RV2 a/c compressors used in your cars do not fare well under the higher pressures of the R134 refrigerant conversions. There are still shops that will service R12 systems - if you do not have one out in your area, there is one in the Ontario area that does. R12 isn't cheap, but neither are rebuilt compressors and even those much of the time are junk to begin with.
Good luck!
