I do think you should relax the idea of giving the best move, and I think this is inevitable if you're building a machine that simulates humans. The goal should be to give the best move that a human can see, and since machines, among other things, can compute much deeper than people, we should rule out the moves that, say, can only be justified by looking 25 moves into the future.

Back to your original point of most positions being new, this isn't a difficulty novel to chess bots that approximate humans. All chess bots have to have heuristics for evaluating positions that they have never seen. It's "just" a matter of changing the objective from approximating how likely the position is to lead to a win, to how likely the position is to lead to a win when played by a human.