Credit where it's due
I have used AP several times for *A award booking, transferring Amex MR points on each occasion--I have no AC status or earned flight miles whatsoever. I must say my experience with the AP agents has been uniformly positive over the years, especially compared with the often grumpy and uncooperative types at US Scareways and United whom I used for the same purposes when they were MR partners.
I usually travel from WAS to BKK or SIN in F/C and these itineraries take time to piece together--a 90 minute call is not unusual when first checking the many possible routing segments and premium seat availabilities--and the agents have never pushed back against anything I suggested and have been courteous. We don't always hand out kudos on FT, but my experience with AP leads me to do so.
As to the best times to call, I have had no waits when calling midweek during midday business hours.