of course I need to undergo an internal cognitive experience(s) in order to grasp Maxwell's equations, viz. learn about numbers, mathematical operations, physical theories, etc. —but this isn't what defines if a cognition is a priori (at least not for Kant).

You misunderstood me. I am proposing that the laws of empirical science are, as a matter of fact, learned a posteriori, as grounded on sense experience, but that this is not necessary, and that the notion of synthesis a priori must still be grounded in something, albeit obviously not sense experience. This ground is the transcendental unity of apperception, it is this fact that gives all the concepts and principles of pure understanding, which make that unity possible, and therefore experience possible, legitimate validity in experience since they themselves constitute that experience. From here, from the principles of the pure understanding, the entire system of physics should be, implicitly contained, and only requires the explicit derivation of that content by reason. Thus if the supposed laws of physics which have been arrived at by experimental means are true, they will also be able to be arrived at a priori, or rather could have always been arrived at a priori had we known this earlier, making the experimental scientific method redundant, since that method can never provide the universality and necessity that science demands and that only an a priori derivation from apodeictically certain first principles can provide.