Jerome Gambit: Is A Draw OK?

The following game treads a familiar path, yet I wound up settling for a draw. It raises the standard Jerome Gambit question: having sacrificed two pieces, should White be satisfied with a draw?

Playing an opponent rated about 100 points above me, this time I agreed.

perrypawnpusher - aansmar

Italian Game tournament, Chess.com, 2024

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ 

4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Kf8 

7.Qxe5 d6 8.Qg3 Nf6 

I have also faced 8...Qe7 in perrypawnpusher - frencheng, blitz, FICS, 2010 (1-0, 17) and 8...Qf6 in perrypawnpusher - kashifnaseem, blitz, FICS, 2011 (1-0, 34). 

9.d3  

Or 9.Nc3 as in perrypawnpusher - klixar, blitz, FICS, 2007

9...Qd7 

Alternatives: 

9...h6, as in perrypawnpusher - caterwaul, blitz, FICS, 2010 (1-0, 39); or 

9...g4 as in perrypawnpusher - salla, blitz, FICS, 2010 (1-0, 18) and perrypawnpusher - marianomocoroa, blitz, FICS, 2010 (1-0, 14); or 

9...Kf7 as in perrypawnpusher - klask, blitz, FICS, 2023 (0-1, 47),  perrypawnpusher - PasayDefence, Piano Piano, Chess.com 2021 (0-1,28), perrypawnpusher - truuf, blitz, FICS, 2011(0-1, 32), and perrypawnpusher - Abhishek29, lichess.org, 2019 (1-0, 35); or 

9...Nh5 as in perrypawnpusher - maxmi, blitz, FICS, 2010 (1-0, 42); 

9...h5 as in perrypawnpusher - ulisimbolon, blitz, FICS, 2016 (0-1, 22); and 

9...Be6 as in perrypawnpusher - Sarantes, Let's Play the Italian Game, Chess.com 2018 (1-0, 37) and perrypawnpusher - GuestTYQD, blitz, FICS, 2023 (1-0, 39). 

10.h3 

This was an unfortunate move to have to make, but I did not want to see Black's Queen come to g4, for an exchange. Still, I initiated the exchange a half dozen moves later. Go figure.

10...h5 

To harass White's Queen. It opens the g5 square to White's Bishop, but Black sees it as worth it.

11.Bg5 Qf7 12.Nc3 c6 

Keeping White's Knight off of d5.

13.Na4 b5 

Encouraging White to make the exchange that he was already planning. Even at the cost of a pawn, the best line was 13...Bb4+ 14.c3 Ba5 15.Qxd6+. 

14.Nxc5 dxc5 15.Qd6+ Qe7 16.Qxe7+ Kxe7 17.e5 

Winning back material.

17...Be6 18.exf6+ gxf6 19.Be3 

19...c4 20. dxc4 Bxc4 21. O-O-O Bd5 22. Rhe1 draw

A draw might seem a bit premature, given that I was a pawn ahead, but exchanging the Rooks on the e-file seems likely, and the resulting Bishops-of-opposite-colors endgame looks pretty balanced.