So I'm an absolute idiot and forgot the bathhouse yesterday... Is there a way to pay CSC to restore your streak? I don't want to go back to the bottom-tier rewards...

Nope. Once you lose your streak, you have to start over. There's a group that pings out a reminder every day though.

The rewards are on a 30-day cycle, so even without breaking your streak you would get back around to the early rewards.

The thread itself is locked, but I use this one for keeping track of what prizes go out on which days: What did you find in the bathhouse pool?