No secret phrase, just frequent repetition of what I was asking for and why I thought it was reasonable, plus a lot of signaling that I was very dug in on this issue.
Basic sequence that played out over many conversations and many days was:
Me to 1-800-GM:"Car's busted, can you tow it to my dealer where I live?"
->Roadside assistance:" We can tow it to the nearest dealer for free, but if you want it towed to a Charlotte dealer you have to pay $450"
Me to service advisor at SC dealer:"Since no loaner car or rental car is available, it seems like a very reasonable goodwill accommodation to transport the car back to Charlotte for me once it's fixed"
-> Service advisor:"We'd never transfer a vehicle , that's crazy talk"
Me to service manager:"Dealerships transfer cars to other dealers all the time"
Service manager:"Ok, sure we could do it, but we're not gonna pay for it"
Me to case manager:"GM can't get parts to fix my car, and you can't supply me a car to drive which is a benefit I prepaid for as part of the CPO program, so how about you do a simple, common thing and transfer the car whenever you do finally fix it."
Case manager:"There might be something we can do for that, let me check"
-> Roadside assistance:"Good news! Since your car broke down more than 100 miles from home, you qualify for vehicle re-unification, I'll connect you to the re-unification department" (yes, there's actually a department that takes care of this)
When I was feeling snarky, I would tell them it really doesn't matter when they fix it, it's just going to sit at that dealership forever because I have no transportation and 130 miles is too far for me to walk.
Anyway, I'm not anti-GM, and really think it would likely have been a similar experience with other car companies, but it seems like such an unforced error to further piss off customers by not being transparent about what they can offer and generally not appearing to give a crap how long it takes or how it impacts their customers.
I'll stop whining now - I am very aware how fortunate I am that this is just an annoyance for me (we have other cars to drive) and realize this could be a real crisis for a lot of folks to suddenly lose their sole source of transportation.