There's a weekly contest at the Washington Post called the Style Invitational that may be of interest to our Speccie crowd, though the prizes are smaller and the opportunities to submit rhyming entries are limited. For what it's worth, check out
this link.
You can get weekly email notice of the new contest by sending an email to
myerspat@gmail.com asking to be put on the list.
I've glanced at some of the names of the winners and recognized very few of them. Ed Conti often triumphs, and I saw Mae Scanlan (a frequent Speccie winner, I think).