""Have I just found a new cure for sick AC???""
Not really, but you have extended the "time/temp" failure a little.
The real problem is the clutch gap. (yours is probably around .040") The wider it gets the more current it takes to engage it. It will pull in fine when cold but as all the temperatures rise (ambient, under hood, and clutch winding) it will fail to engage because there is not enough magnetic force to overcome the wider gap. The hotter the clutch windings get the higher the wire resistance gets and thus less current is allowed to flow in the clutch ultimately creating less magnetic force. Got the picture? When you raise the voltage to the clutch by connecting directly to the battery with a relay and eliminatine all the drops in the wire and connectors, you are pumping more current into the clutch and creating a little more pull-in force.
I went through this a few years ago and actually still have the relay and wiring harness that I used. It got me through one summer but the next it started to fail when the outside temp got up around 90F.
The solution is to remove the clutch plate and take out some of the siims to reduce the gap to <.020. This will extend the life of the clutch/compressor for many years.
I'll send instructions directly to your email.
Good luck.
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Tom 69-1800S, 72-1800ES, 96-850T,2000-S70 GLT-SE