I've been back and forth with that serial number and I actually think it is B36. I think B for "barrel" which is its shape. I know Kent used K for "keyhole" shape so B would make some sense. Anyway, I happened upon a thread on this very forum:
https://www.theshavingroom.co.uk/community/threads/vintage-kent-shaving-brush-catalogue.51316/
See B36 in the list?
Not shown in the picture, so I did a little more digging and found a thread over on The Shave Nook from a fellow who took ownership of a vintage B26:
http://shavenook.com/showthread.php?tid=56018
I'd say that's the mysery solved ... even if you weren't looking for specifics, I'm a dog with a bone when it comes to hunting down this sort of thing.
... but to answer your other question, I'd say YES! Pull that manky old mixed badger knot and drop in a lovely Cashmere Synthetic, which I wager would suit the shape and colour very well. I'd say that the hole should be widened a little so that the knot is closer to the edges of the top of the barrel - this might well help accomodate a modern knot, which is often quite large nowadays. 24mm might well be just right.
On the subject of renovation, under no circumstance try to steam the knot out. The Butterscotch will entirely discolour. Also, no harsh chemicals and no abrasives on the handle which again will remove the Butterscotch colour. At most, I'd maybe go at the recessed discolouration with a wooden toothpick, but otherwise enjoy the "patina" as part of the joy of a vintage brush.