One interesting line of research, I think, is using 1 or 2 layered networks to 'simulate' more complex evaluation functions. If you could train such a network to get within a 10% error of Stockfish's evaluation, then you might be able to distil that network as a faster evaluator to plug back into Stockfish for an even stronger engine. As you say, one hard problem is probably finding actually interesting positions to sample for the training.

Anyhow, it's fun to see how engines like these battle it out. It may also be that your approach can yield a more 'fun to play' engine for us mortals.