Some pins had gotten pushed in far enough that they ripped up traces, so it was necessary to reroute their connections from the bottom vias.

To be able to solder to the vias, you have to scratch the solder mask off of them with a sharp tool like an Xacto knife.

Then it can finally be soldered to with a high gauge wire. I took a section of larger stranded-core wire, cut it, and unwound it.