You need to be a AAA member and have a membership card to use AAA rates.
Sometimes you get lucky and see a promo/package rate on the Starriott website that's a good deal, such as a restaurant credit for more than the difference in rates.
Is Plat guaranteed 4 pm late checkout in the new Bonvoy program or is it just 2 pm if available?
Generally, OP should look at T&C carefully to see whether Bonvoy Plat benefits are worth 35 nights and dealing with current Starrriott customer service and website problems.
In almost all foreign destinations, definitive prices are stated in the local currency. US$ rates appear as a courtesy and are based on current currency exchange rates, which of course can change significantly.