Also, to clarify... Triple Shot+ gear is a little confusing in that it doesn't give Triple Shot when the JA is not active (like melee Double/Triple Attack gear). It only increases the proc rate of Triple Shot when the ability is already up. Same goes for Double Shot.
For COR JSE cape, you're gonna want to shoot in that anyway so it's all good. But for stuff like Oshosi gear, Relic +3 hands, and Empy body: for Triple Shot purposes, you'll want them in your midshot set only when Triple Shot JA is active.