IDK, Heat shrink tubing's entire purpose is to prevent grounding out. Unless it shrank enough to force your signal and ground leads to touch I can't see it being a problem. Either way, I'm glad you got it fixed.
FWIW, if your plugs are getting hot enough to melt the adhesive on electrical tape, you have bigger problems than a messy plug.
Also, there's no telling what's happened inside your new MIC plugs IF you overheated the weld. It may not have hurt the jackets, but could have damaged the inside of the plugs themselves.
Yeah, maybe the heat shrink closed up the gap between the wires in the plug, but I dont think so. 1 cable the gap was a bit close so maybe that was the one that was losing signal strength.
Re Heat... I have a good soldering station with a 70watt Hakko heater in it, so the welds where done fast, the plugs and welds are fine, im sure the cable insulation is fine too. I had to up the temp to get some heat into such thick cable.
Re the electrical tape.. I live in Australia which is what I ment by the glue comes of in heat, not that I'm melting it with an iron. I hate the stuff, if I have to repair a join that I've used it on years later, its come lose and the glues made everything sticky. Its just nasty.
I dunno on the heat shrink.. I know its supposed to an insulator, and that may be true with voltage and strong signals. But pickup output is such a week signal I have a feeling it was rolling off some top end. Which would make some sense knowing a little about very expensive Hi Fi cables and the time they put in to developing dielectric coatings, and supposedly that the top end tends to travel down the outside of the cable... but that's a discussion on best kept for the audiophile forums. I do know good cables do make a huge difference in high end Hi-Fi, thats why I making up some guitar cables with Mogami cable and gold plated copper plugs ( even if they where MIC ).
All fixed now anyway