I use 2NT in sandwich position to show more distributional two suiter, 2C as usual michael's and 2S as natural. So this is easy 2NT - 4D - 4H - 5D or something similar. I'm also totally for always showing two-suiters when possible. The good thing it does for your bidding which hardly anyone ever mentions is that after overcaller bids a new suit, it's always 4 cards. So with this auction, I might be tempted to pass that 3D too. (although I would have doubled 2S so I'm not in the same situation)