I really would separate 'favourite author' from 'best parody', as Marmin says.
But I would certainly choose an author with whom I was familiar. of the 4 you mention, I think Thomas Hardy & Ian Fleming lend themselves best to parody (indeed, reading IF now, he feels like a parody!)
I think you might have fun with IF struggling to write a female Bond, and keep giving her the typing to do.
Thomas Hardy would lend himself to parody the modern southern 'posh' village.
Have just realised it doesn't have to be a parody - but I can't help with that!
And Witzend - another Pym fan here - just wonderful!