Hello, Oh Man. No wonder this confuses you. All your sentences are correct. I'm inclined to view "both" as a conjunction here that serves to coordinate two things, "you" and "Jack". I also think a good argument could be made for "both" as an adjective; however, I'm not sure that this interpretation can explain why "both" can take so many different places in the word order in these sentences. I'll be curious to read what others think.
Speakers often use the other person's name before "I", "you", etc. as a matter of courtesy. There's no "rule" saying that you have to use it this way: Jack and I both enjoy steak. = I and Jack both enjoy steak. Saying "Jack and you" doesn't sound odd to me. Neither does saying "you and Jack".
I think in the sentence above it's considered more polite to mention the other person first, especially to avoid the ungrammatical "me and Jack enjoy". But I guess if you're talking to someone, the person you're talking to should be mentioned first.