I don't have the patience for midi to the point that I prefer to learn to play the instrument and live record it than try to use midi if they're my only choices.

That said, I think you are going to struggle getting a really good approximation of David's sound there unfortunately, since it's a live grand piano with at least two good directional mic's. Your best bet is just finding a GP set with reasonable ambient reverb. You'd almost have to spend time on every single note to get the same sound though. You'd be better off spending your time renting time on a gp and recording that...