desu I push the reincarnation idea as I really hate the notion that LSS/BSS is just a genetic mutation, as then anyone could get it (via breeding/genetic manipulation) and it would be reduced to the same level as the Super Saiyan bargain sale.
Reincarnation was about the only thing I could think of that would make it unique, yet allow for both Kale and Broly to have the form.
Since Broly isn't part of the main canon, it would be easy to say that the last time that this soul was incarnated, it was as him in U6
This would also make Broly the character canon, but not the movies.
Which I would argue is a good thing, because only the first one was any good, and the whole 'legendary super saiyan' could be done better, and this is the opportunity to do so.