Ordered the Brush. Thanks Andrew.
I hope it works well for you.
My method of use, in case you're interested:
Hold it with light pressure against the spinning LP, across the entire diameter for a couple of rotations. You'll be able to see any dust or fuzz collecting in the bristles.
While still applying light pressure, draw the brush slowly outwards until it's off the LP.
Use the hinged bracket (there is normally a foam pad mounted to it) to wipe the bristles a few times back and forth.
Then I repeat the above one more time to remove any remaining dust and you're good to go.