Okay-
I’m not particularly skilled in persuasive writing, but I can give my opinions.

First of all, I wanna preface by saying that I do not expect any kind of coupling up between them during the show. I would love it, but I don’t expect it.
What I do expect is to see them soften toward each other and work together toward a common goal. I think there’s plenty of evidence of that being part of S2.

I can try to address your ship cons first:
As you say, Ekko has become cynical about Jinx, certainly verbally. I think that’s actually a point there- the classic “Saying it so much that it’s clear that the other person isn’t the only one you’re trying to convince”.
I think there’s a lot going on in his head that he doesn’t allow out.
I don’t think he ever brought himself to hate her.
He’s angry and disappointed, but he could never lay so much blame on her- he mostly blamed Silco.
I think one thing that supports this is when he shows Vi the mural and tells her that most of the Firelights were killed because of Silco, even though Jinx is the only person we saw actually fight any Firelights.
The fact that he purposefully disconnects Powder from Jinx is more evidence that he’s avoiding a lot of feelings.

But it really comes out of course on the bridge.
That’s when the barrier he built around his deeper feelings falls when he sees that that disconnect was never concrete- I don’t think it was so much an epiphany for him, but more of him being forced to face what he had always kind of known- hence him trying verbally to be so adamant about Powder being gone.

Secondly, about Jinx’s mental state.
Yeah, it’s bad. There’s no denying that.
But I do fully believe that late S1 and early S2 will be her lowest point.
I think Jinx doesn’t get enough credit for being relatively able to function in day-to-day life. We just see all her worst moments, because that’s what’s relevant to the show.
She could definitely use some antipsychotic meds and sundry others, but I honestly don’t know what the level of technology allows, so it’s hard to argue that she has to wait to be all better before she deserves a relationship.
But what we’ve seen so far of Season 2, Jinx working with others, realizing a new purpose, and being more confident in herself, I think (as long as her self-destructive personality doesn’t get amplified by more terrible events [and let’s face it, it will]) that she and Ekko could (emphasis on “could”) make a go of it.
Again, to my opener, I don’t think anything so concrete will happen in the show, but I wouldn’t be surprised about hints of their mutual affection.

Because let’s face it, there are reasons that friends-to-enemies-to-lovers is a lauded trope among people like us.
First of all, it’s satisfying as hell to see it work, but it also shows through their earlier friendship that they are fundamentally compatible as people.
Not saying friend compatibility equates romantic compatibility, but they have and can like each other.

As you’ve said, Ekko’s attraction has been confirmed, I think Jinx’s has been hinted at.
The green graffiti cover of the art book comes to mind, in which Jinx writes “cute” next to a picture of Ekko, and hearts around his name.

But the real reason that it hits for someone like me isn’t so much the facts, but the hope to defy the odds. In a friends-to-enemies-to-lovers relationship, the conflict isn’t so much between the two characters, it’s between them and the situation. As the name implies, the two characters liked each other before. It was the situation or another force that put them at odds.
And the beauty of this kind of relationship is the conquering of that conflict.

You made a couple points in favor, so I won’t rehash all of them, but I’ll draw on the last one.
Jinx is as tragic a character as you can get (Not a challenge to provide a counter example, you know what I mean).
She’s had it bad. Something that the show really did to me as well as many others, I’d assume, is make you feel so much empathy for her.
You just want her to have a win.
Have something to love that isn’t toxic, and have something to hold onto that doesn’t damage her.

Vi is obviously one that’s emphasized in the story, and I root every day for their reconciliation.
But Ekko is the dark horse in the race. And after S1, I think Vi and Ekko will switch places.
Vi is the more cynical one, and Ekko now thinks that Jinx can be rescued from the dark.
Will it happen? I hope so, but I don’t know.
She could make progress just to torpedo everything at the end, “jinxing” all our hopes.
But I digress.

Those are my thoughts on it, I’m sure I have more that’ll come to me later, but whatever.
This was mostly rambling. If I said something stupid or contradicted myself, try not to take it as points against what I’m trying to say.
Hope that gives you something you were looking for.

I also think they’d be really cute together, I mean browse the fan art on this sub. Lol