Alas. I wish I knew how to message to everyone.
Tribal feelings are very very strong in times of crisis, even if it is those feelings that are causing the crisis.
I do think I have a pretty good idea of how to convey information to the set of people who you seem to mean to be talking to, which are the non-zealots with some compassion for their fellow humans.
But I don't know how to bring everyone along. Not everyone wants to be brought along. It feels good to belong, to be right; it feels good to demonize the other side, it feels good to be on the side of virtue. It feels so good that some people will allow themselves to become so deluded that they turn into monsters; many more will resist that pull, but they will forgive and discount the monsters on their own side.
For example, you wrote a piece a month or so ago that, viewed in isolation, was more stridently anti-Israel and got a pro-Israel commenter saying you believed in fantasies. Then, more recently, you wrote one that criticizes both Israel and Hamas, and you got an anti-Israel commenter saying you believed in fantasies. Whether you were factually correct or not isn't my point here: in both cases, their language was harsh and uncharitable. They weren't really listening.
I don't know what to do about that.
I do have three principles that I think help reach a larger set of people--not the ones whose tribal identity trumps everything else--while preserving intellectual integrity.
(1) Unify. Make as much as possible about universal values, about wanting the best for everyone, about reciprocal kindness, etc..
The killing of civilians inflicts a terrible emotional burden on all sides. How can you ask a Palestinian mother whose children were killed by a bomb to forgive Israel when she did everything she could to save them, including evacuating when and where Israel asked? But also--how can you ask an Israeli citizen to view that woman and her children as fully human if they know that they supported the war that killed them? Nobody deserves emotional wounds like these--certainly not the wounds of the survivors, but not the wounds of the "victors" either.
(2) De-escalate. Avoid contentious language that particularly provokes any side that's worth talking to, favoring inarguable and/or more neutral language. Sometimes imagining (or reading) what someone more on that side would say (or says) is a good way to check.
Israel is precipitating a horrible and avoidable humanitarian catastrophe in Gaza by choosing a rapid war in a heavily-populated area as its primary method of response to Hamas' attacks. (Note: no mention of genocide, no mindreading of the intent of the Israeli government, no leaving out why they say they're doing it.)
(3) If a claim is contentious, but you know it to be the case, have the evidence at your fingertips. Sometimes it's appropriate to offer it immediately (as a link), sometimes only if challenged. But if people ought to know something that they don't want to believe, they're unlikely to take your word for it. (Waiting for a challenge that indicates that they might at least be open to believing, if it is in fact the case, is probably fine.)
Palestinians in Gaza and the West Bank do support Hamas even in their brutality. For instance, in the immediate aftermath of the October 7 attacks (October 31-December 7), an Arab World for Research and Development poll of 668 Palestinians reported that 64% of Gazan Palestinians (and 83% of West Bank Palestinians) answered that they "somewhat" or "extremely" supported Hamas' attacks on October 7 (about 3-1 in favor of "extremely" over "somewhat").
(Aside: the order and nature of questions probably increased that number substantially from what it would have been if it was asked point blank.)
Now, fair warning; this is not the way to reach people the most strongly. For that, you need strident language, passionate displays of emotion, to make things personal/individual (or tell stories about individuals), etc. etc.. Depending on one's proclivities, this might be authentic. (Or it might not--one can put on an act, too.) But I fail to see any path for a strident approach to work at all, when the other side (whichever other side) can just plug their ears.
Finally, I just want to point out that the NPR article is one that I've previously read. It doesn't support your language that Israel's policy is to target civilians, only that they are going to target Hamas whether or not civilians are killed too.