It would be interesting to see how strength and "human like play" scales with the depth of the search.
There's also a really interesting possibility in training policy networks with different attributes by using games from players with certain styles of play.
Training different policies in different styles is a really interesting idea. You could then have a gating process that first chooses the "style" of move to make and then uses the style-specific network to select a move.
I think getting data for this could be difficult though. I wonder how easy it would be to automatically categorize a game record by "style"?
Or, rather than multiple policies, one policy that takes a player vector as an input along with the board position. Players that you predict will make the same move from a given board have their vectors adjusted toward each other and away from a random sample of other player vectors.
If it works, you would be able to perform player vector math ala word2vec. (No idea if it will work)
I don't know a lot about chess, but I would try picking several prolific players with what seem to you to be different styles, and training a classifier to identify the player, as an experiment in viability.
Right now I have just about as close to an "extreme type C" engine as possible. There is a neural network that maps from a board position directly to a ranked list of moves it wants to make., and a little bit of logic on top of that to reject illegal moves.
The recognition of wins/draws/losses is actually done in a layer around the engine, which doesn't understand these things yet. One of "tricks" it is vulnerable to right now is being forced into a draw by repetition, because doesn't know that is a thing to avoid.
Adding a more traditional search (augmented by the network, of course) is on my todo list, and I think it will improve the playing strength a lot. I am pleasantly surprised though, at how well it plays without any of that.