What do you think would/could happen after this position, to leave white even better off?

Well, it seems dubious to me because you sacrifice two pieces for a pawn and you get insufficient compensation.

Based on what, Myko41782?

I think Black's 9...Qxd4+ was overly greedy, and that 9...Qf5 was better (but only based on some database games I found online, I know there is lots of theory about this position but I don't have it).

And now the queen has to retreat (say to f6 or g7), white plays 11.Bxf4 and is threatening bloody murder.

Isn't this the mainline Muzio Gambit?  Did you look it up in, say, MCO?

I agree that Qxd4 was probably a mistake, but after 10...Qg7, I don't see any good continuations for white that aren't just losing. I don't have a good analysis program, but maybe somebody can check the tactics.

The specific line you are refering to is the Double Muzio Gambit.  Your move 8.Bxf7+ is dubious because black can simply hold the material while you have only a queen and king in attacking position.

The main line continues 8.d3! Bh6 9.Nc3 Ne7 10.Bd2

Here is a sample game

Yes, I agree. ...Qxd4 was too greedy but after Queen retreat to f6 or g7, neither I nor my anaylsis program can find a good line for white that isn't losing.