Well, I did successfully get the refrigerator valve (a.k.a Drippy) to stop sweating and dripping. Unfortunately I also got it to stop cooling as well. Sigh. I went back to the manuals I found on the Sea Frost refrigeration system and they do say that if this valve is mounted outside of the "cold box", that it needs to be insulated. They, of course, recommend the cork tape stuff I was unable to ever find, but this foam tape should have been an acceptable, and probably better insulating, option. So it sure seemed like what I did would not have caused this response in the refrigerator.
But, what is step one in trouble shooting any problem: "Did you mess with it when the problem started -> If yes, put it back the way you found it". So, I ripped some of the insulation back off of the valve. When I did, I discovered what might be the problem. Since the vapor line, liquid line, and thermostat probe are bundled together and all run through the same 1 + inch hole into the cold box, I wrapped the lines together. After all, without the wrapping, this was exactly how the system was configured.
The problem is that bundling the lines together actually leaves a small amount of air space in the middle of the bundle. I apparently wasn't able to get the tape to produce an air tight seal for this air space, so the result is that ice then formed in the airspace between the pipes. Now that there is a nice amount of insulation around this airspace, I created what was probably a permanent ice cube. My current theory is that this ice was causing false readings for the thermostat and that caused the temperature to rise in the refrigerator but the rising temperature in the box didn't make it to the thermostat because of the ice.
To test the theory, I used a heat gun on low to melt the ice and I tried to separate the thermostat control wire from the liquid and vapor lines as best I could. The refrigerator is now cooling better...but ice is once again forming on the valve and condensing when the refrigerator cycles off. Since there is still some insulation in place, the cooling isn't completely back to where it was. Guess I will need to dig more of it out and try to re-route the thermostat wire.
Some days, far too many it seems recently, have been of the fixing either not working or the process of fixing results in finding a bunch of other issues. I have to say it is wearing on me more than just a little. The fun to suck ratio seems to be spiraling out of control in the wrong direction during this last push to get things ready to leave Florida.