I was wondering why you are not including Robin in this thread and i quickly got my answer
Naturally she'd disrupt the whole pattern you are trying to establish with the other two about the arc they joined in order to give more credibility to the arguments you are trying to make for Yamato.
Thing is, even if you were sucessfuly able to distinguish Yamato from all three in every single way, it would not matter in the end.
Robin, Franky, Jimbe, all at their time had unique arguments going for them that distinguished them from the previous contenders, that were used to argue in their favor and make claims that they will be different, that this time things will change.
Robin had the highest known bounty after Crocodile, and only 2 mil lower than his at that, and way higher than the bounty Luffy had in Alabasta. She also had feats against the M3 and easily defeated Alabasta's strongest warrior.
Franky did not have the bounty hype, but in his case for the first time a new nakama candidate got a proper fight agains Luffy where until the end they were shown to be equally matched.
Now we move post time skip, and even with the examples of the previous contenders failing, there's hope for Jimbe because :
1. People argued that things have changed post time skip and Oda doesn't care about the M3 anymore
2. Jimbe brought in his own novelty as a former member of the Shichibukai, and certain feats against top tier opponents
No more M3
Jimbe
Sanji
Here at the M3 Club we have a thousand chapters history backing us up, with challengers of all types taking the stage and crashing under the might of the Monster Trio
We're past the point of any doubt, and welcome all to come forth and give their best shot. The stronger the contender the better, as that's merely a new impressive benchmark that Sanji's going to surpass