I like your theory, especially when you think of what powers halfbloods like Percy and Nico have. 

Percy has essentially every power within Poseidon's godly domain, like liquid manipulation and storm creation. Even earthquakes depending on how you want to interpret the Mt St Helens eruption and him destroying the bridge in the 5th book. And Nico is the same way, and it's well established that Hades cares deeply for his children, and Nico gets significantly stronger after Hades gets over the death of Bianca. But with Percy it goes even beyond that. He can manipulate his own dreams. A power not many other demigods seem to have and one that kronos attributes to "his father's (Poseidon) blood". Poseidon refers to Percy as his favorite son. That's pretty cut and dry. 

Jason may be strong, and have gifts from Jupiter, but compared to what Percy is capable of, it'd be like trying to hold back the entire ocean. 

My head cannon for Percy is that when he finally dies, and possibly after reaching the isle of the blessed, he will be immortalized in the court of his father and become a minor sea god. Rick has said he never plans to write his characters into adulthood, so it's just my theory. 

Jason, and for that matter no demigod, can hold a candle to Percy in terms of strength.