Maybe the immediate 1.e4 e5 2.Nf3 Nc6 3.c3 is a better idea if you want a gambit? Not sure about the name (Goring Gambit?). Is a very close relative of the danish.
Against 4...Bc5 if W play your suggested 5.c3 Nf6 6.cxd4 Bb4+ (isn't this an Italian game rather than a Giuoco Piano?) isn't W still in gambit area? For example he can play the classical 7.Nc3 with a Moller attack.
Finally: in the classical lines of the Max Lange (5.0-0 in this move order) i guess the drawish move you refer to is 5...Nxe4. I have seen a recent attempt to revive the line and get a complicated game. if you are interested i can search it and give you a link. The author of the article was a german GM (Bueker?).
I have been playing various gambits (kings, evans, danish) and I decided to pick up this sound gambit.
What are some of white's ideas and goals?