Is anything better for me than the Parham?

That doesn't look too good for white either. As I said, move 6 should be d3.

It doesn't matter, actually. 6.d3 alllows 6...d5, which is also equal.

I'd like to answer both 6.d3 and 6.Nbc3 with 6...Na5, so it's the same.

Sixth move can be either 6.d3 or 6.Nbc3, but the second move shouldn't be 2.Qh5, that's for sure.

First of all, thank you for your insight pfren. Seeing as you actually know what you're doing, could you give me another opening instead? I still haven't found an answer to OP, which is still why I like the Parham. I'd like to just simply have aggressive play, fighting to win position, material, or even mate, but I'd like to keep it sound, preferably not to gambit. Any ideas?

How about the Scotch?

Try the Scotch. Plenty of play for both sides, open game, less theory than the Ruy or Italian.

I've gotten a lot of scotch recommendations. I actually stated in the OP I like it, but can't see how to keep it farily aggressive against:

If it is any help to you, as black I play the Classical Sicilian against e4, and the chigorin variation (d4 d5 c4 Nc3) against the Queen's Gambit.