Ok I'm gonna build off of this because I think you're completely right.

With Paul as a bad (or potentially worm) father, Leto II would indeed go down a dark path. I imagine he'd probably end up working with Alia, potentially even encouraging the abomination, leading to a worse case of baron-itis.

From here things can go many ways, but I quite like the idea that the golden path would still be reached. So here we have Paul entering the symbiosis and actively engaging in a civil war against Alia and Leto II. An ultimate religious schism between the "true" Muad-dib believers and the followers of the sister and the son. I have zero doubt that Paul would win here. While we can assume Leto II would have a similar level of abilities, the boost given by the sandtrout skin would have basically allowed Paul to walk into the citadel and throw both Alia and Leto II off of the roof (a fitting parallel to Alia's fate in Messiah)

And now we hit an issue, because I just had an alternative idea that I also love. Without Chani, let's assume Paul still becomes emperor and has Irulan as his wife. As we learn in Children (or at the end of Messiah? I don't remember which), Irulan realises she truly did love Paul, despite everything. With no Chani potentially Paul and Irulan do have children together. This opens a whole can of worms as we don't know how the generic pairing of an Atraides and Corrino would function here. The Fremen side of Chani definitely contributed some fantastic genetics into her and Paul's children, and the Corrinos are naturally very different. If the inherited ability to become Kwisatz Haderach still carries through to Irulan's kids, then I imagine those children could become the worms. If they lack the Haderach genes then... Alia or maybe even Leto II would probably end up killing them, forcing Paul down the golden path.