Another follow-up-
About a half hour ago, I received a call from a manager in Hyatt's reservations department. She apologized to me for the inconveienence, said that she'd corrected the problem with adding Gold Passport numbers in Hyatt's reservations system, and added my number to each of the reservations.
Hyatt really went above and beyond on this one. Particularly since my Priceline reservation is a super low-revenue proposition for them. I'm very, very impressed.