Thing is, "grammar junkies like Joy and me" sounded incorrect to me; I figured it should actually be "grammar junkies like Joy and I" since one would say "grammar junkies like Joy and I are." Kinda like how it would be "taller than I" instead of "taller than me" because one wouldn't say "taller than me am."
After consulting my pocket style manual, my AP Press style book (which spells "stylebook" as one word on the cover) and The Elements of Style by Strunk and White, I was left confused and decided to call some professionals.
My fiancé is a copy chief at a magazine so I asked him about it, and he said that he thought that using the word "like" as a preposition requires an object, so using "me" would be correct. But he thought he might be wrong, so he got the entire copy department at the magazine on a conference call (incidentally, the copy editors are currently in the midst of closing one of their biggest issues of the year today). Turns out that he was right, and if someone were to use "I" in this instance, it would have to be with the word "as" instead of "like." Example: "grammar junkies as Joy and I are."
The I's Have It [NYT]