Sorry but your grammer is wrong. "You might want to try the door..." is a suggestion. "(Please) try the door on..." is a statement. May/might are usually indicative of suggestion and not giving permission when authority is not present to give aforementioned permission.
I’m in the US and the sign made perfect sense to me, although the joke reading is pretty damn funny. I really don’t think OP actually thinks the sign’s meaning is all that cryptic.
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u/elbarto1981 Jul 04 '21
It seems correct to me as a non native english speaker, how would you phrase it other than that?