StephC, you will get more info by calling so glad that is what you are going to do.
i have the AAA, APH and can use the SMSM/public promo discount.
I always call and see which rate will save me the most money.
last year for my 10 night stay, it was the SMSM rate that was best for me.
the TM's will figure out the nightly rate for the days you are staying and compare it to the other rates that you are eligible to use.
the length of time i am on the phone with them varies.
last year it took about 15 minutes to figure out the best rate for me.
wish you the best for obtaining the lowest rate you can.