The second of your diagrams seems like the best way to represent the conditional reasoning. While it's not necessarily as great as having a specific strategy or precise way of dealing with "but not both" language, there are still things that you can do to flag the necessary material for yourself on the game.
Thus I'd add a parenthetical to the diagram so that "If B does not occur, then H occurs or I occurs but not both" would be diagrammed as:
H or I (but NOT BOTH)
Having "not both" in caps like that can help you keep an eye out to avoid such a possibility.
Another visually useful way of depicting this would be to have another rule taken in conjunction that has B
on the left side of the arrow, and an H-I not-block on the right side. With those two rules, you'd know that B
implies H or I, and you'd also know that B
implies that you can't have an H-I block.