What if the roman gods still switched back and forth between their greek counterparts but they dont remember their greek memories besides a fuzzy memory in the back of their head and vice versa.
I still want HOO to happen, and I think Hera was the one who really set everything into motion? (Haven't reread in a hot minute) But what if she was the one to do so, how about switching Jason and Percy was because she felt a slight pull telling her to do it; voices in her ear from Juno.
Mainly I came up with this for the angst factor because when Percy reaches Camp Jupiter and everyone figures he's the son of Neptune. I want Mars to show up after the War Games and say he is not of Neptune. That kid is war, he is destruction to life as you know it. When Mars goes to look at Percy directly he gets this intense headache that leaves him screaming and clutching his head.
This whole idea sows more seeds of distrust between the Roman's as well as the Greeks, because if even the gods don't know what's going on, then the world has truly gone to Tartarus. Why bond together? When you can follow history and be Greek vs. Roman again.
Jason's split between Greek and Roman can reflect the the Roman and Greek gods: an actual division. Jason is torn much like the gods are actually torn between two realities that they can barely remember from one form to the next.