Thanks for the help. I searched for "Priceline," and found tons of useful and interesting information.

I called GP customer service again and, unfortunately, they told me emphatically that, because mine is a priceline reservation, they are no permitted to append my gold passport number to the reservation. That seems to go against what I read on here about others' experiences, but there you have it. She told me that GP adding my number to the LA priceline booking was "an oversight."

I'd hate to call a 3rd time for fear they put a nasty note in my record, so I guess I'm stuck?