Sigh. Limit short rest in a different way - ie Hit Dice. You know, 5e's true short rest limitation. Once a character has used up their HD, short rest no longer benefits them. Something LIKE this.

The point is that you wouldn't be hard limiting short rest but having unlimited long rest. That's backwards. Short rest should be used more often than long. So you need to create more purpose for short rest, and adding Exhaustion would do just that, and so would Hit Dice as opposed to a 2 limit system.