Here's a short one. Get comfortable.
Finding the fuse was the first step. Without going into a long ditail of the wiring, you can see that was the problem there. I agree that the low side cutoff is not the problem. In the 70 you have a thermo limiting fuse. It's a three connector samll plastic box. When the pressure is low, the limiter blows, and the compressor will not run again until the limiter is replaced. I used to have a spare supply of these in my tool box. But your compressor runs, so that is not the issue.
He is correct that parts are not readily available. But they are available. Most of the suspect components are in the VIR (Valves In Receiver) assembly. The VIR is located in your right front fender, behind the wheel well. Not easy to work on due to it's location.
The VIR contains the dryer, sight glass, expansion valve, Pilot Operated Absolute (POA) valve, filter screen, all the freon control components. Freon goes from the compressor to the condenser, to the VIR high side, to the evaporator in the dash, back to the VIR low side, and returns to the compressor.
The A6 compressor we have in many of our C3s, including yours (and mine) is almost bullit proof. Almost. It's perhaps the best compressor ever built. The fact it kicks on and you can see freon flow is a positive. The fact that one of your hoses gets hot is another positive. That means there is a lot of pressure in the line. So we know the compressor is working.
Freon is interesting stuff. In a flowing state, it's temperature closely relates to it's pressure. This is by no means completely accurate, but the general rule of thumb that does work and in reality works very well, is that one pound of pressure will be one degree in a working system. This is to say 100 PSI is about 100 degrees F. 225 PSI is about 225 degrees F. Again not exact, but fairly accurate. In some ranges its exact. That why your line gets hot. There is flowing pressure.
This also means you system is mostly blocked, not completely. Other wise you would not see freon flow, and you would not have a hot line. The temp would not go up unless there was flow. Granted, there is some flow just filling the line up to pressure, but the high side pressuere drops to low at the VIR, and that's where your sight glass is, unless you have two of them. A few do.
When the pressure drops from high to low at the thermo expansion valve, the temperature drops and the pressure drops. The expansion valve does this. Any restriction will do this as well. So your blockage is at the point where the temp drops.
Follow the hot line with you hands until you get to the point where the temp drops. Check all the lines. When the temp drops, you found the point of your restriction.
It will probably be in the VIR assembly. Hoses and other components can clog, but that's usually from the system decomposing from the inside out. You could have a clog in the evaporator in the dash, but not as likely. The condenser in front of the radiator is not clogged or you would not see the freon flow in the sight glass, and the line get hot.
Any component can decompose from acid in the system. Acid is a result of moisture mixing with freon. Moisture is the killer. The acid can destory anything. But if your system still has a fair amount of pressure, there is probably no moisture, and no or little acid. IF the system was very low, moisture is likely.
Due to the fact the system has not been used for a while, my guess is the components in the VIR have stuck. Again, you can tell this by temp drop. If only the line from the condenser to the VIR is hot, the thermo expansion valve is the likely culprit. If the line from the VIR to the dash, and back to the VIR is hot, the POA valve or screen is the culprit. If you feel a drastic temp change in a hose, there is the clog, and look for deteriotation of the system due to acid. You could have the compressor deteriote from wear, lack of oil, or acid, but yours works so we are not looking there. If you open the system and finds bits of metal, replace the compressor. I don't expect this.
All of the oil in the system circulates with the freon. No freon circulation, no oil circulation. So an unused system does not oil the VIR valves. I suspect long disuse in a dry condition have caused the valves to stick.
The VIR can be removed from the car and serviced. The valves and desicant, the screen, can all be serviced (replaced). While is is possible to do in the car, as hard as it is to remove the VIR assy, it's easier to remove it and service it than it is to do it in the car. You have to half remove it to service it anyway. You may want to just replace the VIR assy as a reman or new unit. Then all you need to do if make sure the system is clean, install the VIR, and charge it with freon.
You may want to look at some of the Corvette suppliers. They have an update unit to replace the VIR, and convert the system into the newer style fixed orifice and accumulator system. This works well, and has less to go wrong in the future. You use the same compressor. If you want, you could even change over to R134a refigerant at this time. That will slightly reduce the out put of the car, but it will still be cold enought to do a good job. Sooner or later we won't be able to get freon (R-12). I'm a long way from that point, but I will do this to my car when I get there. You don't want to do this if you are keeping everything original.
If you do decide to switch to R134a, dont' flush the lines. Just blow them out. The 134a particle is smaller than the R-12 particle. It can leak through a prefectly good R-12 hose or seal. The old coating inside the lines and seals will stop the leakage. You can also purchase stop leak for 134a that works quite well.
So how does A/C work? First you must remember heat and temp are two different things. Just like gallons and temp in water. Also remember we cannot create cold, we can only remove heat.
The compressor compresses freon to a high pressure gas. Keep in mind this rasised the temp a lot. The hot gas goes to the condenser, and is condensed to a hot liquid. The pressure remains the same, but due to the air flow over the condensor, the hot surface gives up a lot of heat volume. This causes the gas to turn to liquid. The high pressure hot liquid go to the designed restriction. This is the thermo expansion valve, or orifice. At this point, the restriction causing the pressure to drop, which also drops the temp. It's now around 30 to 40 degrees, depending on the system, and about 30 to 40 psi.
This cold low pressure liquid goes to the evaporator inside the dash, where hot air from inside the car blows across it. Due to the fact it's cold, it absorbes heat. By absorbing the heat, the air passing through to the inside of the car becomes cold. When the freon absorbs heat, it expands (evaporates) back into a gas. Remember the properties of freon. It's still cold temp. The cold gas goes back to the compressor, where it is pumped to a high pressure, and high temp, containing lots of heat it absorbed in the car. It is now again a hot gas that hits the condenser, looses it's heat, turn to a liquid, and around again.
How do you get moisture and acid out of the system? Evacuate the system, which is putting a vacuum on it. This drops the pressure, makes the water evaporate, turn to a gas, and gets sucked out of the sytem. You need a good vacuum pump for A/C to do this.
Neat huh? It works well.
Let me know what you find and I'll help out as much as I can.