Unfortunately, the experiences described in this thread are the norm at BA, and not the exception. (And before the BA-can't-do-wrong crowd jump on me, I have flown 50 sectors on BA in 2016, down from 59 in 2015. I think my sample is large enough to generalize.)
What beats me is that BA finds it so hard to get this right. Queue management is not rocket science. If AA can do, surely so can BA.
To add a new observation to this thread: BA's penchant for outsourcing ground handling to contractors like Menzies at outstations doesn't help. The likes of Menzies don't seem to be aware of BA's current priority boarding policies, so they call premium cabins and gold/silver/bronze/aluminium/tin all at the same time. That's so 2014.