Minto As the motor has been out of the frame, make a check that the sprockets are in line, maybe a loosen of the mounting bolts and a little tweak just to get things straight.
BSA Service Sheet 212C recommends that for Plunger Models, the bike should be on the stand, rear suspension at its lowest point. Half an inch total up and down movement at the centre of the span is the figure suggested.
In an ideal world the chain tension stays the same as the wheels sprockets and chain rotate. Usually wear and other factors mean that there may be tight and loose spots. Best to adjust the chain at a tight spot so no undue strain is put on the transmission.
Its tricky to do, keeping the wheel central, sprockets in line, chain tension the best compromise, so don't get too frustrated if it takes that little bit longer to get right. Easier to move the hub and drum if brake rod is disconnected.
Don't forget to tighten the big nut securing the drum and then adjust the rear brake once the wheel position has been set. Off the stand the chain will be at the accepted running tension, slightly looser than set on the stand.
On the stand sets the chain tension at the suspension's greatest point of deflection, so appears to be relatively tight, but the geometric relationship between the sprockets changes off the stand to give the running tension. This relationship change is more on a plunger frame than on a S/A. Plunger axle moves in a straight line, S/A moves in an arc, so here , suspension loaded is the better method of setting.
By my reckoning the chain was a bit too loose with 1 1/2" on the stand, even looser when running, enough to throw it off if the sprockets were offset.
Swarfy.