Now, thematically, if I were to make just one of them a buff job, and knowing what I do of their history in this game (had I known nothing of how XIV planned to implement each or seen only their ability names across the multiple languages, I would likely have gone with making SCH the buffer instead, but w/e), yeah, I'd make AST the buffer over SCH. But...
At the same time... does Chain Stratagem harm SCH's identity through its inclusion? Is it mutually exclusive with some other, more "XIV SCH-like" action that SCH would/likely could otherwise have had? Does it harm AST's, WHM's, and SGE's by association? I am not convinced it does any of those things.