If you are going to have just one really good lockwasher it should be on the left side of an SA AW, since the axle is stiffer left of the sun pinion than to the right.
For the lockwasher setup to work there are four requirements
a) that the axle fits the dropout OR that there are two tangs on the lockwashers
b) that the tangs fit the dropout
c) that the axle flats are a snug fit in the lockwasher
d) that the load is shared between sides
There is no such thing as 'a standard SA lockwasher'; they make about a dozen different sorts. In most installations the high gear torque is not so high that the axle requires positive restraint, so the usual thing is that the axle rotates backwards in gear 1 and then stays there. However if the axle is not a good fit such that the reaction torque causes the axle to sit lower in the dropout slot than normal in low gear, the axle will move around between gear 1 and gear 2 let alone gear 1 and gear 3.
SA lockwashers have various issues;
- standard powder met ones (with two tangs) fit well but crack too easily
- thin wrought steel ones are a bit flimsy
- single tang powder met ones are more robust (because they are thicker but can still crack
- thicker wrought steel ones don't always fit the axle perfectly
- 3/8" sized ones fit RX series 3s hubs only
So if you want a robust setup then using up to four HMW518 washers on an AW 3s hub is possible; you can use two each side, one inside the dropout , one outside, with the tangs facing in opposite directions, or shortened and facing in the same direction.
being wrought material they won't break easily and can easily be modified to fit most frames.