In terms of sport specific training, my hunch is that the 2h swing is ''the best'' move for judo and the 1h standing military press is ''the best'' for fencing (also helpful in judo).
This is all just by feel though training and experimenting with kettlebells since 2014 alongside judo (since 1988), the fencing is only 2 years old for me as of yet however.
Overall GPP I could say I get in many ways through just the sports themselves, although they lack enough strength building that the sports actually need, which is of course totally ironic and ridiculous, but hey, the real world is like this!
The irony is that judo does not make you strong enough to do judo and fencing does not make you strong enough to do fencing (well).
Judo needs full body power pulling, and fencing needs ''strong'' balance and strong bent arm strength.
In any case, I asked the original question because it just dawned on me that if SF did not put a cap on ''just two moves'', SF might come up with something just as good but different, and I was curious as to what that might be.
I have started to spread the gospel of weight training amongst my fencing teammates while improving my own fencing with kettlebell strength. The judo community knows all about kettlebells and SF, and several at the club train specifically S&S, me included!
The full power hip hinge is critical in judo, I think at least, and this is best hit with the 2h swing... just as the 1h standing military press pretty much replicates the strength system needed for fencing. the TGU has stuff in it that is not needed for fencing, but is good for judo newaza (ground wresting), and the 1h swing is excellent for overall grappling strength, but it does not seem to recruit enough power for the insane effort you need to actually throw an intelligent and strong opponent in many cases, and you absolutely need both hands for this (with of course a few minor exceptions as there always are for anything.)
...However... at least with the 2h swings, it seems to me more about drilling the movement than about relying on the 2h swing to develop any strength I wouldn't have already gotten from the S&S 1h swings, which deliver strength in large quantities! Same for the 1h presses vs TGUs: the TGUs grant more than enough of the same kind of strength, but there is an important and subtle coordination carryover to fencing benefit by doing 1h military presses.
I have no conclusion to all this yet - just my musings at the moment... (if anyone cares, haha!)
