… Kick Mingo's ass, safe the country, and approach all of the relevant members of the Reverie with true story in secrecy?
Let's see, with the toys freed, and marines and goverment agents among them he should have about complete story of what Mingo has been doing. Plus Birdcage, and the entire plan to murder a country and all that.
And then I would be like "Yo! Those Shichibukai guys? Big trouble, correct? Not worth the hassle? Cobra-san agrees, yes? How about it: You take their status away, and I'll knock them down with my fellow Admirals, and they will never take over your countries or try to murder your citizens. Sounds like good deal?"
What does anybody cares about public opinion? This is authoritarian state; public opinion means jack shit.
And yes, it is better for Fujitora. Because, and lest we forget, Kings are public figures. Everybody knows them. So if Fujitora would approach them with their plan now, me, in their place, would answer like that: "Yeah, we will take away their privaleges, that they have enjoyed for many years, and they will want revenge. And as Dressrosa has shown, you can't protect us. So we rather deal with them not trying actively murder us, thank you."
The entire abolition relies on Goverment being able to effectively deal with Shichibukai, with whom they will be at open war the moment they take away their positions. And if you don't think they actually can, why would you vote for it?
If the kings of reverie are actually rational, Fujitora could have very well just doomed his entire project, because nobody will trust him that WG can actually get rid off Shichibukai's safely, and not collapse under combined might of them and Yonko.
I knew this would be your reply but think about this what is happening now on dressrosa is very similar to what happened in alabasta and I think your solution would just let things end the same way. The only difference between the two situation are 1. In the first case the warlord was trying to take over the country by framing the king and putting is royal soldiers and citizens to kill each other, while in dressrosa case the warlord succeed by murdering a member of the royal family and use they king and his men to kill innocent citizens and burn the city. 2. The second thing is that one was using the royal guard and revolutionary army to kill each other and if that fail he would use a bomb to kill them, while the other the king and his men (Doffy) is the one trying to kill the citizens. Both these situations are different but similar at the same time and therefore I think if Fujitora was to step in and take care of Doffy it will end the same way only difference this time is that they wouldn't need to give one of their own the credit knowing that he wasn't the one that defeated the warlord but this time it was actually one of their admiral. The long and short is that they will get the credit, take away Doffy privilege and replace him with another.
Now I think that even if Fujitora were to say call on the kings for support only one would probably join him and that is Cobra, due to his country going through a similar situation dressrosa is going but bear in mind that this is not a must as the Straw Hats were the one who aid him plus their is probably some beef between Cobra and the world government stemming from ancient time (speculation) which may make him not rely on them. As it relates to Doffy and his dirty dealings I think that is one thing the government wouldn't want known and they will most definitely want to shut up Fujitora as this will only let them look weak in front of the world which can cause nations to rise up with more confidence and disrupt their power grip. Remember they went as far as to cover up the escape of the wanted criminals why would you think they wouldn't do the same with Doffy. They depends on the warlord system and they will not just let it go because of one warlord we have seen this over and over therefore it will take more than what you propose seeing that it is basically the same as what happened in the past they would rather replace him and cover up the information about his black market dealings. I think there is more towards Fujitora'so plan we just need to be patient.
One thing I want to leave you with think about who he is gambling on Luffy the pirate that have been a thorn in their side from the beginning starting from the defeat of a warlord to the destruction of impel down to the great war. Imaging the world this time knows about what they did for a country rather than the Marines this time, think about what that will cost them seeing they will not be able to cover it up this time. They would need to buster call the entire island. I think this card is a good one for Fujitora and it is apart of his strategy. Anyway I am using my phone so I may have some typo plus it is hard to follow my own conversation.