Any number of things could be conditions of experience, e.g., the brain, the sense organs, the nervous system, etc., but none of these things have anything to do with the transcendental ideality of space and time, they have nothing to do with the categories, in fact they have nothing to do with anything that Kant was talking about -- at all. In order to show why this is the case, I'd like to provide a brief explanation of what Henry Allison terms an "epistemic condition."
An epistemic condition is a condition that is necessary for the representation of an object or an objective state of affairs, and thus it is in virtue of such conditions that our representations relate to objects. Epistemic conditions are different from logical conditions of thought, e.g., the principle of contradiction. While the latter serves as a condition of consistent thinking, the former serves as a condition of the representation of objects.
Epistemic conditions must also be sharply separated from physiological or so-called "psychological" conditions. Custom or habit, as used by Hume in his account of causality, is an example of a psychological condition. While physiological or psychological conditions may be necessary in order to explain the origin of our beliefs and perceptions, or even of our knowledge "in order of time," they cannot account for its objective validity.
But the question of the validity of our knowledge is nothing other than the fundamental issue raised by Kant's Critique of Pure Reason. If Kant can show that space, time, and the categories really are epistemic conditions -- and I have provided a strong argument that at least the first two really are epistemic conditions -- then transcendental idealism follows. If Kant cannot isolate and display our epistemic conditions, then our conditions of knowledge must be construed in psychological or subjectivistic terms. (In other words, there is no knowledge at all.)
But anyone who merely insists, without meeting Kant head-on, that our fundamental representations are psychological in nature, never really addresses this question at all. Facing up to the issue of epistemic conditions leads us to a more accurate interpretation of Kant, and it allows us to understand the true intent and nature of transcendental idealism. And I hope I have convinced many of you by now that when one does this, one finds it to be a powerful philosophical position indeed.