Needing help to make bagpipes authentic; URLS of applicable theory explained?

I've found a good set of Highland bagpipes, Uilleann pipes, and other Celtic instruments that I'd like to use in an arrangement of Holst's "Thaxted." However, I'm struggling to find instruction on exactly how to use the drones — particularly in that, given my limited knowledge of theory, I don't quite grasp how a drone can just go on and on with apparent disregard for the key of the melody (and harmony). I've played the drone part as a root of the chord as I'd expect it in conventional western (= American) music, but — and here's where I become especially confused — it seems that the drone should actually be even more dissonant.

If you can take the time to explain how the drone should relate harmonically to a given piece (e.g., "Thaxted" as attached), and/or if you know of any URLs that lend insight, I'd be most thankful. (Also, separately, I've posted a request for pointers on using the church organ most effectively; if you're knowledgeable on the king of the instruments, feel free to search by my name for that piece and respond there likewise.)