I'd actually be quite interested in seeing conservatives writing things which mock conservatives. It's probably true that we're generally fine with liberal caricatures written by liberals because they're written from a place of understanding. Conservative caricatures of liberals fall flat because conservatives really have no clue about liberals, which is why they're always trying to piss us off with things that don't actually piss us off.
But a good conservative caricature written by a conservative would probably teach liberals a few things about how conservatives see themselves.