Just stick to " Guten Tag" and you´ll be fine everywhere in Germany !
(even in Bavaria - where Gruss Gott basically is the "norm")
I agree. "Guten Tag" is certainly the most appropriate approach. Even I as a native (western) German speaker refrain from using "Grüaß Gott" all the time. And "Du" is certainly perfectly all right under the circumstances you described.
I understood you wanted to be polite so "Howdy" certainly not on the agenda and no native German speaker would use it.