meowmeow, thanks for your reply.
Perhaps I should have clarified this in my post: I am obviously not asking about my personal situation since, as my signature info shows, I already have a green card.
This question relates to someone else who has not yet applied for a GC and whose 6 year H1B limit is expiring soon.
So I would still like to know: is it possible to change status from H1 to J1?