I read through much of this thread before calling the BA call center, to prepare myself for what to expect. After a close to half hour hold, I got a knowledgeable agent who didn't have any problem with getting me booked on the flight I wanted. Very professional, and was able to see the correct amount of seats available with no issues. It went fairly quickly and the agent specifically mentioned that the $25 call fee was being waived, as he said the award was impossible to book online and that I'd just be charged the $5.60 in taxes. Very happy with that.

The one thing I have a bit of issue with is not giving an Alaska confirmation number. Fortunately I was able to find it by going to checkmytrip as suggested in the thread and putting in the BA confirmation, but I can see how troublesome that could be for the less experienced flyers out there. Overall a good experience, but you'd think they'd save time and money by having some sort of online booking option.