Andy, thank you for a very creative suggestion!
I was thinking last weekend about how to, perhaps, give the CSS a bit more "food". Contacts are clean. I have 12.4V on CSS when engaged, seems enough, but... What if I sourced power to CSS from a "clean place" through the relay? This is what I read for me from your post. Hydraulic switch would turn the relay on by giving it ground, and relay would give power to CSS.
Hooking a CSS for transmission electrically through the back up/starter firewall switch does not work well as the signal you get to CSS comes too soon and CSS kicks off before the gear is engaged causing: rev up then gear in. You can use it as emergency when your transmission switches are gone.