Is it not so that the set of possible actions a Kantian could perform is a subset of the set of possible actions a Utilitarian could perform?

It depends on how you want to describe actions. So, on the one hand a good Kantian will never lie while a good utilitarian might, on the other hand a good utilitarian will never minimize utility, whereas a good Kantian might.

Kant and your average utilitarian will disagree not only about on-the-ground ethical questions, but about questions like 'what is an action' and 'how are actions individuated' and 'what constitutes the "consequences" of an action'. This makes translation between the two theories difficult.

If this is true, could not a Utilitarian decide that Kantian behavior is optimal for maximizing utility, and thus emulate a Kantian's behavior in any given situation (similar to Rule Utilitarianism)?

Absolutely, though it's hard to see what sort of utility calculation would conclude that Kantianism is going to optimize for utility in any given situation. Kant is explicit that the actual consequences of an action are totally irrelevant to its moral value. So it would be one heck of a coincidence. Needless to say, the Kant-emulating utilitarian would never be fulfilling her moral obligations in the Kant's eyes, regardless of how complete the emulation is. For a Kant, it's important that actions be motivated (or at least constrained) by a respect for the moral law; returning the jacket out of respect for the moral law and returning it in order to maximize utility don't even count as the same action so far as Kant is concerned, since the maxims differ.