Jay is a really cute nickname and J.P. would also be nice. I really like the nickname J.J. (jay-jay) for a little boy and I know his initials wouldn't be J.J. but it would definitely work with any J name I think.
I could see where you might not want to use the obvious
Jo but what about Chim or
Kim? Or you could be creative and call him Mich (or
Mick) from the -chim part of his name.
Liking
Jay best though!
Hope this helps to give you some options!