I think some flowchart planning will really help here.
If this were a book or a movie, you could precisely plan out how the characters will act. In a game, though, it's frustrating as a player to not be able to effect the outcome.
I notice in your plan, though, you have a few different ideas of how this will play out, which is good!
I would be less concerned with how the scene actually plays out, and focus more on how you can communicate consequences to the players. Any action they take should have consequences. You can have it all lead to the same follow-up scene (characters have to get by without the king), but still let it play out as consequences to the characters' choices, not despite their choices.
So, for example:
If they try to cure the king -
The vizier warns them that approaching the king without his permission is a crime.
The guards will try to block them while the royal physician is summoned.
The king will look worse and worse.
If they don't approach -
The king will get worse and worse.
They will head whispers from others in the court, wondering why they don't take actions.
They will see someone running away - if stopped, this person is a spy or a messenger or something, but not responsible for the poison.
If they cure him -
He is whisked away to a secret chamber.
He quickly whispers or sends a secret message: "Act as if I have died, I will send word!"
They hear whispers from others in court wondering how the characters knew and we're prepared for the king's poisoning!