There was a wonderful Radio 4 series called News at Bedtime which sent up the nursery rhyme and fairy tale world. And with material such as Hey Diddle Diddle to work with, spoofing was a gift I would have thought! If you ever get a chance to listen to this series, do so. It's hilarious and stars Jack Dee and Peter Calpaldi (prior to his getting the call to "pilot" the Tardis in Doctor Who).
I do have a soft spot for the nonsense verse of Lewis Carroll, Edward Lear and Spike Milligan. Couldn't write it but love reading it. Having said that I find I can only read it in small doses at any one time? Why? Because for me the world of fantasy still has to be believable. When it goes into pastiche, it, for me, literally loses some of its magic. What do you think?