Hi Steve,
There you ARE
I think you have found a (maybe not the?) problem
Before you go levering on the conrod, carefully check the small end bush for being bored /reamed off square
Get hold of a pair of engineering parallels and a length of 3/4in. ground steel bar (silver steel is ideal)
The 3/4in. rod should slide though the small ends, if they are in line then the rod should pass through both ( happy days)
Rod bend can be in two planes, inline with the crank and twist
Place the parallels front to back either side of the conrod, If the piston is machined square at the bottom it should rest evenly on both sides
Cut 4 strips of paper and place these under each contact point between piston and parallel
hold the piston down onto the paper strips with a finger of one hand in the centre
use the other hand to gently pull on the strips, when all is good the pull should be even all round
If both loose on one side then bend to correct
A trickier situation is where the strips are loose diagonally, turn the crank over so the rod is opposite angle
and check again. If the loose strips change diagonal position then the small end is twisted
When you are confident the rods / small ends are good pass the 3/4in. rod though both the small ends, if they are in line then the rod should pass through both ( happy days)
If the pistons are cutaway on the bottom, you have to rely on the gudgeon pins sitting on the parallels
Then I had a memory flash back
Last year, I was asked to look at and solve a similar issue to your bikes on an AJS 650 twin, But it smoked on both a bit and blew oil out the breather
All the above testing proved all good, bore to piston clearance was within tolerance and new rings had been fitted a year or so before but the problem remained
I noticed side to side rub on the pistons, at the outside on the bottom and inside nearer the top??
I set up each cylinder on parallels on the mill and Mcgyvered a DTI onto the side of a bar held in the spindle
Testing for "squareness" by raising and lowering the mill table in front , back and side to side
I found that both bores were "Off square" side to side to the base by 6/7 thou
The owner has had the bike since the early sixties and never had it rebored in his ownership even thou it was +.020 ?
A very careful setup by my rebore guy got the cylinders true on +.040
I hope the BSA problem is in the small end bushes not in the cylinder for your sake
John