Your engine has a high compression piston fitted,(7.5:1?)
the usual LC were flat topped
It has a long rod, easy to spot as the pin is near the bottom ring
The bore is toast, I know they will run with grooves and scores but you are never going to be happy doing a half arsed job
The +040 rings were a bodged attempt to sort it then sell it on
Get the engine shop to remove the valves and check the valve and guides as these are more than likely needing attention as well
New valve springs are also advisable
Regarding lapping the head, the inner face is the recess in the head and the top of the lip /spigot on the cylinder
The outer faces are where the head bolt holes are on the cylinder and head
In the video of the bike "running" I can hear a lot of gear noise
This is common on B31/33's when the magneto gear is too tiightly meshed with the idler pinion
This is caused by wear on the mag platform and magneto body
It can be sorted by shimming if not too bad,
The magneto strap tends to pull the gears tighter together
Sometimes an alloy strip can be placed between the front strap and magneto body to keep the gears correctly meshed
The mesh is correct when a strip of paper can be passed through the gears without it being cut through by the gear teeth
Of course the "correct" method of reclamation of this probblem involves welding and remachining the cases and restoring the magneto body to original, mucho $$$$$
In the video you posted the engine is eight stroking and misfiring, and reluctant to rev
If this was soley rich mixture there would be clouds of black smoke from the exhaust
I suspect a magneto problem ?
I would have the magneto checked out while you have the engine apart.
Sorry to be the bearer of all this "bad news"
I have both a B31 and B33 engines in the workshop at the moment
The B31 was sold to the current owner as "done"
He was "done " allright, !!!!
the engine was totally worn out but still just about able to run, after a very few miles it packed up
The B33 bore was totally worn out on max oversize, It has now been resleeved back to std, I had difficulty finding a Std high comp piston