FYI, a rebus using punctuation was published
in the NYT more than five years ago, so it's possible that they rejected it on that basis alone. My feeling is that with rebus puzzles, you have to try something that they've never done before because a) the NYT is one of the very few publications that actually uses them and b) they use them somewhat infrequently (i.e. usually only on Thursdays and maybe the occasional Sunday, and even then, they don't use them on most Thursdays).
As for other publishers, I'm not aware of others who accept outside submissions that include rebus grids. But if you happen to be under the age of 30, you could try submitting it to Ben Tausig's "Twenty Under Thirty" app. Read more about it here