King's Gambit transposition

Hello all - I've just been experimenting with transpositions from the bishop's opening into King's Gambit lines, with decent results up to now. I was hoping to get some analysis to check the soundness of some of these lines.

Typically when I go for such a transposition, my opponent elects to go for the declined variations of the KG, however in a recent 2 min live game I had, my oponent allowed me to create more along the lines of an 'accepted' transposition, which worked to my favor:

Nice!

What would you play on 3...Nxe4?  That's not very King's Gambit-y.  I actually play a similar system occasionally, where I open with e4, Bc4, d3 (in response to the typical Nf6), then a quick f4.  If it goes 1.e4 e5 2.Bc4 Nf6 3.d3 c6, I respond 4.Qe2 instead (4...d5 5.exd5 cxd5 6.Qxe5+ retards their expansion), and get in f4 as soon as I can.

Granted, it's not really very King's Gambit-y either because I can (and usually do) immediately recapture Bxf4 if they exchange there, but I'm fond of it.  It's not the sharpest for White, and Black equalizes comfortably with best play, but it's unusual enough that it gets people out of their booked-up comfort zones, and they tend to drift.  Fun for variety, at least.

It's usually a much slower game, though -- your opening seems much more in the spirit of the KG, if not the actual moves.

 Ok, a couple things to address here:

I am very much aware of the fact that the 3. d3 line does not lead as consitently to KG type games, as I have already tried that variation several times, with mixed results.

Indeed I do find, as you have said, that those games tend to be longer, and more positional, but part of the KG is to create more open and tactical games! (That's why I like it so much!) So as such,  I find that you have to risk something to get something, and that if you want a tactical and more open game, sacrifice will be necessary.

To answer your question, what will I do after 3. ... Nxe4 and there are several options, but let me show one with a nice trap that I've stumbled upon in my investigations and experimentations:

Indeed, after replying to that last post, I was inspired to try out this latest live game. I punished my opponent for trying something different:

Here is another recent live game of mine where my opponent actually resigned due to the tactical possibilities alone! (and also being down 2 pawns). This game highlights typical/possible tactical scenarios and motifs that are likely to arrise during such King's gambit transposed games: