First of all, it's April Fool's Day. I initially thought this was a trolling post, but I think you're legit. I actually do have a recommendation for you, but let me address some of your questions first.

Severitus is popular for several reasons. One, it is feasible. Lily and Snape were buds and if things had gone just a little differently he might well have slept with her. Alternatively he could have forced her into it either via potions or just using force.

But even before we knew of that relationship, it was interesting b/c of the animosity between Snape and Harry. Forcing them into a blood relationship has the potential to add a lot of interesting drama that doesn't exist with Sirius for example.

Sirius is already acting as Harry's father figure. James is long dead. So how does Sirius being Harry's real dad really change anything? It could, but it's just not that interesting. It's a moot point.

Remus has potential because he might have had a legit reason to hide the child -- he's a werewolf. Teddy doesn't appear to face persecution because of it, but it's possible in a different generation Harry would have.

But for the most part, giving Harry a different parent seems lazy/boring unless it's being used to drive the plot, and most of the plots driven by that sort of thing just aren't up my alley anyway. They tend to involve too much angst.

This is halfway a crack!fic, and Lockhart isn't Harry's 'real' father, but he did raise Harry so perhaps it counts: https://www.fanfiction.net/s/6635363/1/When-In-Doubt-Obliviate

But anyway, here's a halfway decent crossover with Naruto. I can't think of any pure HP ones. This is a series of three fics where Harry's father was Hatake Sarumo.
https://www.fanfiction.net/s/3777014/1/A-Personal-Matter
https://www.fanfiction.net/s/4313529/1/Sphere-of-Influence
https://www.fanfiction.net/s/6534243/1/Extending-the-Boundaries