I'm wondering how all the sweat got down inside the rear brake. Maybe traveled down the brake housing from the stem area? Who knows...
So you routed the brake housing from the rear brake all the way to the lever itself without a separation at the steerer tube? The front brake was also an issue for me as the tight bend in the low far config made the front brake always tend to rub on 1 side. It drove me insane until i figured out that i needed to bend the wire in the opposite direction so there was even tension on both calipers. If its working for you I would not touch it hahaha!
Try the brake wedge trick. It might fix this entire issue for you (move the brake wedge up .5-1 inch further up the wire)
Also I know this might be beating a dead horse, but use a towel or 2 always indoors. I have done this and I have had no issues with my bikes other than a replaced fork bearing set, but I think that was due to just how much riding I was doing and some wet races.
Edit: If you have the housing in 1 shot it should be easy to replace the brake cable and seeing if it helps. TBH I would consider doing that or buy an el-cheapo wire (like 4$) and seeing if it does the trick. Shouldnt take more than 10 mins if your taking the entire thing apart anyways and if its in 1 shot, its a quick swap out