I obviously haven’t mapped out every possibility in my head yet, but the idea would be that with the Gods favoritism for the Trojans and Hector just being a beast, he wouldn’t be killed but wounded heavily (my idea that he loses all the fingers on his sword arm catching the blade while still in bed) enough that he could be killed by Patroclus.
Achilles is still said to be destined to die in the Trojan War though, so the major diverging point from here would be if he takes credit for the kill as himself or as Achilles. If the former then Achilles dies later on while Pat lives, if the latter, then he dies ‘as Achilles’ and thus making the prophecy come true in a sense and giving Achilles a chance to survive the war.
So unfortunately I think Pat and Achilles are destined to be tragic lovers in one way or another. It’s simply the Greek way.