The following principles are both plausible.
Between any two events, ideal observers should prefer that the one that makes the world better occur.
If an ideal observer would prefer one take some action, they ought to take that action.
But these entail
Between any two actions, one should take the one that makes the world better.
But this is consequentialism. If one action makes the world better than another, you should take that action. Thus, given that on all remotely plausible versions of axiology, it’s better for one person to die than five, this entails one should kill one person in Transplant and should push the person off the bridge in Bridge.
2 seems obvious. It’s just so abundantly clear that if a perfectly moral third party should want you to do something, you should do it. God—if he existed—should not want you to act wrongly. The correct set of preferences involve wanting people to act rightly. Richard has also shown that this is the only view that supports real normative authority.
1 is sort of intuitive on its face. It seems plausible that one should prefer better things happen rather than worse ones. And we can prove that in all sorts of cases, a third party should prefer right things happen to wrong ones. For example, Richard has shown that third parties should prefer one kills one to stop two killings. But from this we can derive all sorts of other preferences. Surely they should rather one kills one to stop five deaths than two killings. So the results in organ harvesting and bridge fall out—as do the results in the sheriff case. From this we can derive that one should take any heinous act to prevent multiple other instances of the heinous act. There is no even remotely plausible non-consequentialist account of what third parties should prefer.
The first principle uses the word "should" but the last uses the word "would". I'm going to assume you mean "would" in both cases, since presumably what any observer *should* want is identical to what an ideal observer *would* want.
That said, we need to define what we mean by "ideal" or "perfectly moral" observer. There are two plausible definitions that I can think of. However, both definitions imply that one of the premises in the argument is a trivial, analytic truth and the other other premise is question-begging.
On one definition, an ideal observer is just an observer who wants everyone to perform right actions. In that case, premise 2 is a trivial, analytic truth whereas premise 1 is question-begging against deontology. The premise "Between any two events, ideal observers should prefer that the one that makes the world better occur" would be equivalent to "Between any two events, [observers who want everyone to perform right actions] would prefer that the one that makes the world better occur". But this alone is sufficient to imply consequentialism. Why would this premise be compelling to someone who didn't already accept consequentialism?
On another definition, an ideal observer is just an observer who wants the world to go best. In that case, premise 1 is a trivial, analytic truth whereas premise 2 is question-begging against deontology. The premise "If an ideal observer would prefer one take some action, they ought to take that action" would be equivalent to "if [an observer who wants the world to go best] would prefer one to take some action, they ought to take that action". But this alone is sufficient to imply consequentialism. Why would this premise be compelling to someone who didn't already accept consequentialism?
You point to some reasons for the premises in the later paragraphs, but they are unintelligible without defining what an "ideal" or "perfectly moral" observer mean.