This may be a case where I just got it wrong, but to me it never made sense. 

If Dany dies and Hizdahr is king, the Shavepate is a dead man and his entire revolution is destroyed. If his objective was to do a false flag operation, why not do it in a way that implicates Hizdahr – say, by having some of his Brazen Beasts attack Dany in the name of the Sons of the Harpy and Hizdahr King? Why not do it BEFORE Hizdahr marries her and gets political legitimacy? Hell, if he wanted to get rid of Hizdahr, why not have Hizdahr assassinated and blame that on the Sons of the Harpy? That would solve his political problem much more directly.

Look at the chain of events that happened in OTL – you have a poison intended for Dany, that only gets revealed because she brings Belwas with her and Belwas goes hog-wild on them before she even touches them, then the dragon shows up and Dany leaves, then Hizdahr replaces Dany’s entire team including the Shavepate, then the Shavepate has to sell Ser Barristan on a coup. Ridiculously circuitous doesn’t begin to describe it. 

So it’ll take some explaining in TWOW if that’s what happened.