Seems like a really messy gambit, with good chances for both sides.
Ponziani Opening: Jaenisch, Vuković Gambit

After spending a day evaluating this messy opening, I believe that I have come up with a line with white which is somewhat forcing and easy to memorize. It end up in positions which stockfish evaluates from 0.00 to +0.3. Most ponziani players tend to be more aggressive than me, I would rather want a questionable advantage than an absolute mess of a game. Here is the lines that I came up with, which I believe simplifies the position.
If anybody has any lines that I have missed for black I would like to hear them.

After spending a day evaluating this messy opening, I believe that I have come up with a line with white which is somewhat forcing and easy to memorize. It end up in positions which stockfish evaluates from 0.00 to +0.3. Most ponziani players tend to be more aggressive than me, I would rather want a questionable advantage than an absolute mess of a game. Here is the lines that I came up with, which I believe simplifies the position.
If anybody has any lines that I have missed for black I would like to hear them.
This is honestly not a forcing line at all. You need to analyze (and memorize) a lot more in order to make this work in a real game. For example:
10...O-O!? 11.Rg1 Qf6 Black keeps his knight on f2 in order to accelerate his attack.
12...Bf2 putting the bishop on a safe square.
14...e4 trying to open the e-file, at the cost of a pawn.

This is honestly not a forcing line at all. You need to analyze (and memorize) a lot more in order to make this work in a real game. For example:
10...O-O!? 11.Rg1 Qf6 Black keeps his knight on f2 in order to accelerate his attack.
12...Bf2 putting the bishop on a safe square.
14...e4 trying to open the e-file, at the cost of a pawn.
Thank you for your thoughts!
I think I should have been more clear on what my goal with this line were, to simplify and make the game less sharp. For that, I came up with the move 11. a4!?. I tried to edit my earlier comment but for some reason, it would not update.
10... O-O is defenetly another variation which needs to be considered, but this variation start before the move 11. a4 is played. Again, I should have been more clear what I was talking about.
I had not thought about 14... e4 however. But it does not look to difficult to deal with. Qxc5 exf3+ 16. gxf3, and the e-file is open, but I still believe white is better because he has the bishop pair, more piece value (not counting pawns), and I dont see any direct way for black to use the open file to an advantage. I would not consider this to be a critical move.
Your move 12... Bf2 is the best alternative for black I think. The game do remain very sharp. Stockfish seems to want to transport the King to c2. The only problem is that black either has to loose a tempo moving the bishop back, or loose his knight on h1. I think white's best option is to continue to simplify the game, and if he can trade a some pieces, I would rather play white. But tbh I think the 12... Bf2 variation is black's best reply so I will have to look into that a bit more.

I like Nikos Ntirlis's recommendation and I have had a lot of fun playing this line, since it seems that most lower-rated Ponziani players don't really expect such a rare line and the play is natural enough to not be really memorization in my opinion. I must agree however that your suggestion is certainly more practical and simple.
I'm a ponziani player, and a while ago I came across an interesting defence suggested by the computer. The defence goes like this:
1.e4 e5 2.Nf3 Nc6 3.c3 Nf6 4.d4 Nxe4 5.d5 Bc5
After taking some time with the computer my final thoughts were that the defence is only good at pro/computer-level, and that nobody at my skill group would be able to play such a sharp defence to an uncommon opening like the ponziani. But now recently my opponent played it against me and after some unclear and advanced play I lost the game. I want to start a discussion here about this defence. Is there any way of simplifying the game as white? Is it playable for black(/white?)? Has anybody else seen this defence being used?