Been somewhat preoccupied over the last couple of months, but everything finally back to normal so an update on the Beezer issues. In short, it now running like an absolute dream and I am so grateful for all the help. The carburation was WAY out, there were two separate oil leaks and the wet sumping is cured (by a curious little concertina-style ally tube, not an on-off tap). Some of the tweaking was done by Roadstar Cycles, a glorious 1950s-style motorcycle shop in what looks like the old cavalry stables next to Dover Castle. It's like Ogri's workshop - interesting machinery round every corner and a clock above the oil-stained counter which proclaims: It's time YOU had a BSA.
And only 18 miles up the road. Brilliant.
Following everyone's advice I have been running it in with a lot less caution, giving it some mild stick at frequent intervals, and it is far, far better. The smoking left pot has stopped smoking, which I assume means the rings are bedding in better, it ticks over and twitters perfectly and is a joy to ride.
Still running on (new) SAE 30 and planning on yet another oil change after a couple of hundred miles.
Day off today and with English weather almost spring-like (a balmy 10 degrees C and bright sun) spent an hour and half hacking round the country lanes. Although I took a spare pair of plugs and a spanner in my pocket fearing the dreaded soot, it is no more. I haven't whipped them out to check them yet, but am expecting a lovely chocolate electrode. Just in time for Easter.
Again, many thanks for all the help and suggestions. Can't wait to get some serious mileage in.