My engine wiring harness burned up a couple wires yesterday!
Visegrips! Well now you know. At least you checked first to see if they were holding.
What you did should hold. There are issues with soldered joints, but also some advantages. Make sure they are supported and aren't getting strained or vibrated.
For closed barrel terminals and wire Ancor marine wire products are pretty good. They are carried by chain stores such as West Marine. Some West stores also have reels of marine wire in a wide range of sizes and insulation colors. The wire on reels is sold by the foot. The majority of stores have a more limited selection. They probably also have heat shrink tubing - I always buy from McMaster-carr so haven't paid attention. Mcmaster has oil resistant shrink tubing as well as colors and flexible shrink tubing. Which is best to use depends on the location.
A place to mail order wire in smaller quatities is Wirebarn