2711 isnt that far off. It could well be a genuine beavertail drum. 2811 is a genuine beavertail COB Dynasonic. I have it. There are higher numbers that are genuine B&B drums. I have seen some. Transition overlap or mixed up badges in the badge tray? Who cares? Probably both, they built drums and back then, no one was anal about what number was on what drum.
It is a 1963 drum. It is beautiful. And even if it has the B&B changed to Beavertails, it is still a pretty drum. I would play it.