You know how boats can transport players and shulker boxes can transport items by remembering the details of the items inside them? Why not have both? I think shift-right-clicking a boat with a shulker box should add the shulker box into the a seat of the boat, and further shift-right-clicking should open the shulker box normally, if looking at the chest.
Maybe have the shulker box in front of the player, to open the shulker box while in the boat, when necessary. And the same way you would make the boat drop as an item, from the entity it generated by being placed, I think punching a shulker boat should drop the shulker box and leave the boat to either be used normally, or to be punched again to be picked up.
If this is not going to be included into the normal game, I think at least a mod should be made to do this.