Or a new JA: Charm II.
Allows bst to charm normally uncharmable mobs including things inside abyssea but excluding non-animals, beastmen, and nms obviously. Give it as high as 1-2min recast maybe and longer charm duration.
Similar to your idea, but SE could adjust the recast time on a new JA to balance it. And the ability being past 45-49(past 75 more likely) prevents other jobs from subbing bst and gaining the same advantage.