I'm confused, why are we using the Melee roster? You said third-parties are in though, does that mean it's the Melee roster plus Sonic, Snake, Mega Man, and Pac-Man? Can we have Pit, Shulk, and Palutena instead? They'd make short work of the more problematic All-Stars.
Anyway I see a lot of people who don't know how broken Ness is (canonically) in here.
None of the characters you mentioned come anywhere close to Kratos, and the rest of PSASBR would make the tak of wiping out SSB characters even easier.
Ness and Shulk are JRPG protagonists and their power levels are exactly as absurd as that suggests. Shulk is excluded for no apparent reason, so I'll tell you how this plays out.
The only match-ups that matter are Ness vs Kratos and Ness vs Zeus. Nobody aside from Ness on the Melee roster is even close to literal-God-tier, which Kratos and Zeus are. So while Ness is fighting one of them, the other is single-handedly defeating the entire cast of Melee. Ness finishes his fight, maybe he won, if so he gets to fight the other. And then it's over.
I think it's more interesting to take such OP characters away for a moment and look at really weird match-ups. What even is Mr. Game & Watch? How would he fare against a Big Daddy? What would Mewtwo vs Cole be like? That sounds awesome. Can I get some Samus vs Raiden? He'd probably cut her up, but it would be dope as hell. Would it be Kirby or Jigglypuff fighting Fat Princess?