You can always try to transpose the Petroff to a 4 knights with 3.Nc3.
Now after 3...Nc6 (3...Bb4 is also a decent move, where white can get the bishop pair and hope for a small advantage) you can get the 4K flavour that appeals to you.
I suggest the Glek (4.g3) which leads to interesting play after both 4...d5 and 4...Bc5, and the resulting positions are certainly not drawish.
And of course the same system can be used against 2...Nc6.
Aside 4.g3, I have a terrific score as white with the tricky 4.h3!?, but objectively speaking it should be equal with good play from Black.
What are you talking about man? d4 scores more draw than e4 does. E4 tend to be way more unbalanced than d4.
In the last world championship how many games were won with e4 and how many ended up as draws?
Dude, you cant use one championship as a source. I'm talking millions of games from various databases and all suggest that d4 has more draws, less losses, and less wins.