Welp I did the deed yesterday. I stripped down the harness and found all the butt connections were still intact, although very corroded. The blue connection had a few strands broken, but I don't think it was enough to cause a bad disconnect. I cut them apart anyway and soldered them.

On the soldering, the tinnning of the wires went great! I had no idea that would work so well. But it was a mess soldering the two wires together afterwards. I made hooks before I tinned them. Then I put two hooks into the other hook. I put more flux on, then tried to solder by allowing the solder to flow from the tip to the wire (the same way I did when I tinned). This didn't work at all for me, so I ended up heating the wires until the solder would melt directly on the wires. This worked fine, but made for some pretty big joints. I hope they are okay!

I electric taped over them, then electric tape wrapped the whole harness. Then I put black plastic split loom over it, and then electric taped over that. It looks better than factory now. Hopefully these connections will last a long time!