You are right in your feeling that beginning your question with the preposition is more formal than ending with it.
When it comes to some of those longer, less common prepositions, I think forming questions with them is a lot more awkward, and less natural. People would often tend to rephrase the question in a way that would avoid that particular preposition.
In particular the questions you use as examples seem to be so unusual that it's hard for me to gauge which one (of each pair) would sound more formal and which more slang-like.
In the first example pair, people would typically not even form a question using "because of" since we have the word "why" which is specifically intended for that kind of question.
In the second pair, I'm having trouble imagining a situation where a person would inquire about what wasn't used ["What did you do it without?" ... Isn't that like asking how many accidents didn't happen?]
However, from this list of prepositions, there are a couple of longer ones that might be a little more suited to example questions:
"underneath" -- "Which bed did you find them underneath?" or
"Underneath which bed did you find them?" more formal
"in lieu of" -- "Who [whom] are you volunteering in lieu of?" or
"In lieu of whom [who] are you volunteering?" more formal
Although those questions might be more naturally reworded as, "Where, exactly, did you find them?" and "Who are you subbing for?"
In those 2 examples (which sound a little less awkward to me, ... meaning no insult toward your own examples of course), the second choice (preposition at beginning) still sounds more formal than the first.
So, in answer to your question, yes, you do have the same two options for preposition placement whether the preposition is a long one or a short one. And the situation is the same regarding formality/colloquial-ness.