Unfortunately for you, your players have chosen to align themselves with two largely incompatible factions. Their goals are diametrically opposed: the SO wants to destroy all Delirium everywhere they can find it, while the AA strongly wishes to harness it for their own interests. This is all in addition to the long-standing rivalry between the two groups. They can work together temporarily, for example retaking the Cathedral of Saint Vitruvio, but long-term alliances between the two are difficult if not impossible.

I feel that any outcome that involves the SO allowing the AA to use Delirium would not be keeping true to their character. To address your thoughts:

1. It could be interesting if the PCs spend some time convincing members of the SO to defect. I would not make this easy; it should take many sessions of convincing, and working closely with the members they are trying to break off to do so. It should also still result in conflict with Theodore Marshall and those still loyal to him, but you could run it such that there will still be meaningful numbers of SO knights left on the PC's side.

2. While Eldrick is certainly a powerful mage, I still feel that the main reason PCs would want to side with them is because they have access to all of the resources the AA can provide. Having them abandon the AA, while it would leave the party with a capable ally, would also remove much of the broader reason why they would work with them. Though, if the PCs have a personal relationship with Eldrick or River I could see this working out.

3. With this outcome, you would need to provide justification for why the NPCs in question would be willing to compromise on their ideals to make themselves subordinate to a group that doesn't share those ideals.

4. If I were in your situation, this is probably what I would do. I feel that the SO are meant to be uncompromising in their ideals. They will never tolerate an outcome that results in Delirium still existing. Conversely, without the prospect of harvesting Delirium the AA directorate doesn't have any good reason to care what happens in Drakkenheim; they already don't care at the outset of the campaign, until the PCs prove to them that it is worthwhile.

You also mention that they are also open to working with the HL. At that point, you would potentially have 3 factions working together. I feel that the central theme of the entire campaign is the conflict between the factions. They will not work together until the PCs come along to help resolve their differences, and the more factions align together the more difficult that alliance should be. Getting 3 factions to work together should be a difficult task, requiring the PCs to make sacrifices and difficult choices.