IMO this is not a mistake as it’s maximizing all his opportunities. Other than this, he could only appeal to the SC directly or, as you said, rewrite the EO.
This way he’s looking for the small chance that a larger panel from the circuit will rule in his favor to keep the EO intact. Otherwise if they rule to keep it in place again, I suspect at that point Trump will rewrite the order.
He’s just going for the Hail Mary at this point and he loses nothing by doing so. If he rewrote it now, he would be giving up before he had to, and he will have to rewrite it anyway if they rule against him. So there’s nothing really lost here.
I suppose one could argue suffering another legal setback would be harmful for his momentum and/or mandate. So would rewriting the order now (it would be admitting defeat before all options are exhausted) so that’s a push IMO.
It doesn’t hurt to try when all negativites are equal.
Another argument for going before the en banc 9th circuit is that, although they will rule against the EO, they will write an opinion that will help the DOJ write the next EO so that it can address their problems with the original EO. They will agree with the 3 judge panel on due process, but they may write something new, like an objection based on Establishment.