Hi Ron,
I've got a SJ 650 engine in my '56, well I will have, when I put the bike back together. Here's some comments, but not necessarily answers....I think there are differing views regarding the desirability of LJ versus SJ cranks, some think the LJ is stronger and most agree it is less prone to whipping, but the big end bearings might actually be stronger on the SJ (they are smaller diameter but wider). LJ cranks are far more expensive to get hold of.
1. I suggest you check/measure the engines balance factor (to ensure the vibes are not excessive) whether you decide to use a new LJ or your SJ crank. I know many people do not bother, probably as it's not so easy to do and the calculations are a "challenge", but I personally could not put an engine together without having a pretty good idea of what the balance factor is. The other option is to give the job of balancing the crank to an engine builder (but again I personally would still check their work/calculations!). There's a couple of recent threads regarding balancing.
2. You will need SJ con rods to match the SJ crank (I'm using SJ billet rods, which are said to be significantly heavier than OEM rods).
3. I'm not sure what the total weight diffences of the SJ versus LJ crank is, but I would expect the weight you are really interested in (for balancing purposes) will be the counterbalance weight difference.
4. The counter balance weight might very well be the same for the 2 cranks? If the weight of the rods/pistons/pins/rings is the same for the SJ and LJ engines?
5. I'm not sure if BSA altered the balance of the cranks to suit the various pistons the bikes were sold with? Probably not? There is a service sheet on crank balance which from memory states the counter balance weight at 32oz, no mention of differences between the models or SJ or LJ.
6. I suggest you weigh your pistons/pins/rings, you might be surprised at the results, for example, I've found Hepolites to be similar in weight to JP's, and both being heavier than BSA OEM pistons. Generally lighter parts are better for keeping vibes down, assuming the crank has the standard counterweight.
Just my 2 cents worth!
Edit:
Here's a link to the service sheet 712x
http://www.petercomley.com/712X%20Flywheel%20balancing%20static.pdf