In Rosenberg's Accessing Kant, he describes a certain 'Strategy K'. Could anyone succintly explain this strategy for me?
It refers to Kant's solution to the problem of justifying knowledge. After the criticsm of "intellectual intutition" by empiricists two legitimate sources of knowledge remained: logic and experience. Logic however produces only tautologies, or something tautologically equivalent to experience, and experience itself directly justifies little. Hume's argument against induction and causality showed that even most basic inferences lack justification.
One could, and Rosenberg discusses such options in his book, try to find a third source of justification, tertium quid as he calls it in Latin. Husserl's phenomenological intuition is an example, but Rosenberg considers such a solution disappointing. What he describes as strategy K is to change the concept of justification. Instead of justifying the content of a principle theoretically, by providing an argument for it, one can give a logical argument that the principle has some meta-property, making it practically reasonable for us to adopt it.
For example, Kant agrees with Hume that we can not deduce the principle of causality from observations, but argues that we should adopt it nonetheless because it is a condition for having a unified account of experience in time, "condition of the possibility of knowledge", as Kant calls it. He then proceeds to give an empirically grounded logical meta-argument that causality is indeed such a condition (questionable from modern point of view). This does not give us theoretical certainty for the principle, but it does give it a practical justification, and strategy K does not take us beyond senses and logic, there is no tertium quid.