I have heat shrink butt connectors already, plus just regular heat shrink tubing of all sorts of styles and types. IF I can twist and turn my big arms and hands in there, I will try to solder it. I've gone a kick-butt soldering setup that would do it right, but working around all of the stuff under the hood would be that challenge. The crimp and shrink method is probably the easiest and *should* stay secure.
Oh, and glad that the part numbers worked out for you. I was (incorrectly) given PT374 as the part number back in February when I first was looking to fix this. Similar part, but completely wrong as I found out today... (I told you that I waited a long time to try to fix this.) Now I have to see if my local Advance Auto will take it back after so long.