Okay, I've identified the flaw in my understanding of this position. After the natural progression of
10. d3! Qxe5 11. dxe4 Qc5+
At the time I didn't know how to evaluate my options for moving my king appropriately. Both Kg2 and Kh1 allow a similar lines, whilst 12. Kf1 d5 threatens mate from 13... Bh3, and loses a tempo when the king must move to Kg2. You can't use 12. Be3 to block check because it just sacs the bishop.
12. Kg2 d6 13. Nc3 Be6 14. Nd5 Bxd5 15. exd5 Nd4 16. c4 leaves white with a strong advantage both positionally and materially. The same line, but with 12. Kh1, seems to be more or less the same. Is there a natural disadvantage to pushing your king into the corner like this when black loses his white bishop? There is an alternative line of 12. Kh1 d6 13. Nc3 Be6 14. Bf4 Re8f8, but I don't understand why this would be considered superior to moving 14. Nd5 as this seems to allow black a strong presence along the e file.