Has this been tried with reinforcement learning (RL)? As the OP notes, it is plausible from a RL perspective that such a bootstrap can work, because it would be (quoting the OP) "exploiting the generator-verifier gap, where it is easier to discriminate than to generate (eg laughing at a pun is easier than making it)." The hit ratio may be tiny, so doing this well would be very expensive.
Run ML of any combination and form in a for loop for higher order is one of the most obvious avenues. If it worked you would have heard about it a long time ago.
