Thank you OP!

Park Hyatts are not included in the terms. Outside the US, I got no discount at PH Milan or Shanghai. Group # 13365 works at PH Chicago and Washington for 10% off. The PH Washington Presidential Suite drops to only $6204.60 on Thursday June 3.

Looking at Hyatt Regency and Hyatt Place in the US, rate code 13365 returns the same rate (or within a dollar) for Costco Hotel Crdit as the AAA Breakfast summer promo. The cancellation policies look the same, too. It's not prepaid, so Costco certificates work, as they should.
Therefore, the choice inside the US is between full breakfast for 2 with AAA, or a $25 nightly credit with COSTCO/13365.