Oh Jason. Sigh forever.
I'd just have him be another child that Hippolyta had back in the day, either before or after living on the island. Now, I have a hard time seeing the true Hippolyta willingly sleeping with Zeus, but I wouldn't even seriously mind Zeus being Jason's father if it meant that we could just shovel all this demigod stuff onto him, while Diana gets her own separate distinct clay origin. If DC thinks the Zeus origin is so friggin' great, then Jason is welcome to have it all.
My strong suspicion is that someone up high on the WB/DC decision-making branch was doggedly hanging onto the Zeus origin at the time, and even now continues to do so, in order to keep synergy with the DCEU. Which, yeah, is pretty ironic/silly/backwards considering that the movie likely only forced in the Zeus origin in order to keep synergy with what was the comics origin at the time...and also like, who even cares about the DCEU anymore at this point lol. The editorial branch of the WW offices seem more competent and put-together nowadays than they've ever been before, but this remains the one scab they won't pick at, likely also because Conrad and Cloonan don't seem particularly incentivized to do so.
...The downside of which is that this one single discrepancy in Diana's backstory continues to spread out and muddle the backstories of every single
other character in her franchise, from Cassie (whose father Lennox doesn't technically exist anymore) to Donna (created by Amazons who never existed) and even Hippolyta and Nubia as well, so every writer who handles them nowadays has to do the narrative equivalent of politely ignoring the fact that these characters' origins haven't made any sense for about ten years
.