I used to be committed to Halos, but have found that the Headsweats work much better and are more comfortable. They do actually keep you cool despite covering your whole head.

Link to what you use?

This is out of left field, but do you use some sort of energy/nutrition mix in your bottles? I've noticed on occasion, that what is left at the tip of the bottle in the rear cage will "spray" in the wind while riding. In your case, it would appear that this would be all over the rear brake mechanism/cable.

Are you sure that is a stainless cable? If it is, the the problem is probably the cable housing, and not the cables.

I'd look at different cable brands. Perhaps they aren't all the same.

Are you using lined cable housing?

One option might be a dedicated trainer bike, and just go brakeless :)

Another option might be teflon coated cables and teflon lined housing, but you're still at risk once the coatings become compromised.

fwiw.. I like the "Shorty". but not the Super Duty Shorty. It's not clear to me if they're still making the original (non-"Super") version.

Go on Amazon and search for Headsweats Classic Headband or Shorty or Coolmax Headband. It is not a hat but a tie-on headband.