Universalization of maxims

Suppose that I want to see if the following innocent maxim satisfies the first form of the Categorical Imperative:
(1) When a friend is hungry, and you have more than enough food, offer her something to eat.
Kant says I am supposed to imagine (1) universalized into a law of nature. But what is the universalization? Two options:
(1a) For all x and y, when x's friend y is hungry, and x has more than enough food, x offers y something to eat.
(1b) For all x and y, when x believes that x's friend y is hungry and that x has more than enough food, x offers y something to eat.
In this case, both universalizations work--no contradiction (in will or conception) ensues whichever is the one I take to be the relevant one. But there is still the question of which is in in fact the universalization relevant to the Categorical Imperative.

Sometimes something substantial depends on this. Take a case like the one Korsgaard considers. Betty wants to murder George who is hiding in your basement. Betty doesn't know that you know she wants to murder George, and she doesn't want you to know. Instead, with seeming innocence, she asks you if George is at your house. Korsgaard thinks that you can universalize lying to deceitful potential murderers (i.e., potential murderers who are deceiving you about the intentions), because even if everybody lied to deceitful potential murderers, the lying would have the desired effect, because the deceitful murderer would think she successfully deceived you, and hence she would think that you wouldn't be lying back to her. Again, in this case there are two universalizations possible:
(2a) For all x and y, if y is a deceitful murderer, x lies to y about the location of y's prospective victim.
(2b) For all x and y, if x believes y to be a deceitful murderer, x lies to y about the location of y's prospective victim.
For Korsgaard's argument to work, (2b) has to be the right universalization. For if (2a) were a universal law, then deceitful murderers would inductively know that (mysteriously enough) whenever they ask people about the location of their victims, they're lied to, and so the universalization of the maxim would destroy the maxim's effectiveness.

On the face of it, too, universalization (2b) is preferable to universalization (2a), because it's hard to imagine what motivation people have for lying to people they don't believe to be murderers. Maybe, though, in (2a) we are supposed to imagine not only that the maxim is universalized, but that the people know or at least believe that it applies. Thus, maybe, the correct universalization is the hypothesis:
(2c) For all x and y, if y is a deceitful murderer, x lies to y about the location of y's prospective victim out of the maxim "Lie to deceitful murderer in order to save the victim's life."
The universal truth of (2c) entails that in such circumstances, the murderer's deceit is never successful.

So now we have three ways of universalizing--(2a), (2b) and (2c). Which is right? I suspect that (1b) and (2b) aren't the right universalization. First, they mistake the maxim. The maxim is not: "Feed those that I think are hungry" (leaving aside the condition for the availability of food, for simplicity's sake). What gives me reason to feed them is not my thought that they are hungry, but the fact of their biting, unpleasant hunger. It's not about me, but about the hungry. The mistake of thinking the maxim is "Feed those that I think are hungry" is like the mistake of reasoning: "I think that p. But if p, then q. Therefore q." The latter argument is logically invalid, except as an awkward way of saying "p. But if p, then q. Therefore q." The correct maxim is "Feed those that are hungry."

Second, these subjectivized universalizations give the wrong answers in some cases. Suppose I am the doctor in an asylum. It's an odd asylum, however. All the inmates think that they are the doctor, and that everybody else (including me) is an inmate. Consider the maxim: "If you are the doctor in an asylum, prescribe correct medication for the inmates." (It'll need some qualifications.) No problem universalizing this along the lines of (1a), (2a) or (2c). But suppose you universalize along the lines of (1b) or (2b). Then you get everybody who thinks she is a doctor prescribing what she thinks is correct medication for those she thinks are the inmates. And that wouldn't do at all--indeed, it would involve a contradiction in conception, since everybody would be be getting the wrong medication, thereby contradicting the point of prescribing medication. The correct maxim is not: "If you think you are the doctor..."

Objection: Inmates in an asylum do not count for universalization purposes, because they are not rational agents.

Response: Well, tweak the story a bit. They are not literally insane. Instead, they all have some medical problems that require medication, and they have a sanely acquired set of strange false beliefs--they believe themselves to be doctors, even though they are not. (It's easy to come up with half a dozen scenarios where they might come to that belief.)