I don't know very much about scripting, but it is generally possible to bind numbers like the stamina in this script to variables? That way, the player could do all kinds of things to change stamina. For example, I was immediately reminded of Skyward Sword, where you also have a stamina bar. It's used not only for running, but also for climbing faster and various other things that are exhausting, and you could restore your stamina by collecting certain items on your way. All these things were easily doable with stamina being controlled by a variable. :)