First of all, I like this analysis. It's so much more well thought-out than so many other arguments I've seen in this regard, even though it's really kind of inaccurate. For one, I see some categories having higher priority than others. When I say that I mean that some categories are more important than others, and I'd say that makes the overall analysis fairly inaccurate. Also, "plot significance" and "significance" (appearances) should really be merged into one category, but I guess I'll address those separately for now.
Anyways, I see nothing wrong with the analyses of the first two categories. Popularity is hard to gauge (though from what I can tell Junior is the most popular character as of now), so giving them all even numbers here is fair I guess. Appearances aren't something that can be addressed, for obvious reasons. I really only have a large problem with one category: plot significance.
I can see both Bowser Jr and PM given higher numbers here. PM is most likely the most significant to his games out of the three seeing as he's the protagonist of them (arguably the most important role of any game save maybe the main antagonist). Geno is a very important "side" character and Junior's role is inconsistent throughout his appearances, though has had roles as the main antagonist.
On that note, Junior's plot significance, like I said, is inconsistent. That's why I would merge this category with "significance" to make a general significance category. Still, Junior is given relatively low numbers here based on your reasoning for them. Junior is NOT Bowser's pawn, in fact he works independently of Bowser in Mario Sunshine and the New Super Mario Bros (it's also hinted at somewhat in Galaxy). Both of the mentioned appearances I might add, were as the main antagonist of the game, which is very significant to the plot-line (again, it's arguably as important a role as the main protagonist). No antagonist, no plot. And yes, Bowser served as the final boss of both games along side Junior, though there is a difference between "main antagonist" and "final boss." Junior made and enacted the plans to capture Peach in both the mentioned games, making him without argument the main antagonist of both games.
Personally I'd give him the same numbers as Geno here. He's not as important as PM, though only because of his inconsistent roles.
But again, the whole analysis would be so much more accurate if you were to merge the two categories I mentioned. It's because of Junior's so many appearances that I would give him a lower score in this area; if you were to merge the two, Junior's probably the most significant of the three (generally speaking).
And of course there are other variables to take into account. Junior is much more recognizable, he's a more recent character than the other two. The games these characters have starred in as well, which games had a larger impact on audiences? That effects the character's importance as well.
Really, it's Bowser Jr who has the best chances out of the three. Or rather, he's the most deserving out of them. His character has more depth to it than PM or Geno, he's more recognizable, had more appearances, has possessed very important roles during said appearances, and has great move-set potential (paintbrush/pole-arm weapon). Plus, you can't have Bowser without Bowser Jr nowadays, it's innappropriate.
But like I said, while this analysis is well thought-out, it's not very accurate. Plus, we've had so many arguments on this topic, that there doesn't need to be any more. I'm so tired of repeating myself so many times.