Stop jumping the clutch relay. If you pull a vacuum on the system, that alone is generally enough to suck at least a half can of refrigerant in. All you should do at that point is turn the AC on and wait for the compressor to cycle on. I've ONLY ever bypass the clutch relay when I suspect a faulty low pressure switch. You have most likely caused damage to the compressor seals from overheating it.
As to why the can is getting cold: It's when a gas goes from a high pressure to a low pressure, it gets cold. If it's doing this slowly, the amount of gas leaving the can might not change much over time. You seem to still be having an issue getting refrigerant in. If you're attempting to charge it into the low side port, you're doing it right.
Now, you might be able to get it in through the high side while the system is still at a vacuum. If you leave the engine off and vacuum it down through the high side, charge as much as you can into the high side, then shut it off when the pressure equalizes, you might (MIGHT) be able to get the system working. That's assuming your compressor isn't toast. That should be enough pressure to activate the low pressure switch, which will allow the compressor to run. Yes, it's going to cycle. A lot. Start the engine and turn on the AC. Start trying to charge the refrigerant to the low side now. It sounds like the valve has gone bad, but it does allow a little refrigerant to leak by, so it's going to take a while to get it in there. Let it suck the can empty and check the pressures. By the way, I wouldn't really trust the low pressure gauge since it has to go through that suspected valve, so you're going to have to base it almost solely off of high side pressure and vent temperature.