Thanks JB, Tom and ShinyShoes for the comments. I was hoping to get the bike finished this year, but that might not be possible after all.
The brake assembly was in a very rough state, but nothing was seized up.
It was improved somewhat after bead blasting, spraying and baking in the oven.
New shoes and springs were added. The springs are Morris Minor items at a quarter of the price of those listed for the BSA brake. The Morris springs are a little shorter, but they still fit and work fine.
I have two of these wheels to rebuild, so couldn't resist fitting this one to my 250 Victor to try it out.
So with the shadow of how bad these brakes can be hanging over me for decades, I finaly try one out for the first time.
After the first several applications of the brake the screeching, slight juddering and grabbing fades away to reveal a fabulous brake with superb stopping power. Ok, it's only stopping a 300 lb bike from moderate speed rather than a 500 lb triple, but I am more than impressed, and with the air scoop it looks good too. So that's one more decaying BSA relic that's been saved and reborn.
This is the dreadful state of the rim the wheel came with, totally rotted through.