"Peace be upon you!"
So where is the "be"? And customarily, I have seen many possible translations of the phrase, "peace with you", "peace onto you", even just "peace"—although every Muslim I know would never translate it in the first place, even the most recent convert—there seems to be an assumption that God only understands Arabic.
(1) "So where is the "be"?"
In my mother tongue's translation, there is no "be" but it simply looks like "peace onto you" in English. We describe السلام then translate عليكم.
The "be" in English has not only confused you, EvemarieMo, but also me (as a non-native Muslim). Anyway, some says that the "be" in this case is rare, perhaps it is from "maybe" -- "may praise be upon you". (You know English better than me. Why do English translators put "be" there?).
(2) "there seems to be an assumption that God only understands Arabic"
The السلام عليكم was from Classical Arabic, a dead language, was understandable by only Ancient Arabs, who lived 1,400 years ago. If we want to understand this expression perfectly, we should learn Classical Arabic and not Modern Arabic (or dialects).
In short, the problem is in Modern English and not Classical Arabic.