At one point in the first Critique, Kant shoots off this list of stipulative definitions:
We are in no want of words to denominate adequately every mode of representation, without the necessity of encroaching upon terms which are proper to others. The following is a graduated list of them. The genus is representation in general (repraesentatio). Under it stands representation with consciousness (perceptio). A perception which relates solely to the subject as a modification of its state, is a sensation (sensatio), an objective perception is a cognition (cognitio). A cognition is either an intuition or a conception (intuitus vel conceptus). The former has an immediate relation to the object and is singular and individual; the latter has but a mediate relation, by means of a characteristic mark which may be common to several things. A conception is either empirical or pure. A pure conception, in so far as it has its origin in the understanding alone, and is not the conception of a pure sensuous image, is called notio. A conception formed from notions, which transcends the possibility of experience, is an idea, or a conception of reason.
He also uses "active/passive" in his characterization of apriority and experience: a priori judgment is proactive in that we "project" the function of the terms onto their referents, e.g. when we count, we have to actively focus on the things we are counting (though see about subitizers for people who can identify the number of a set of things without piecemeal going over the set in their apprehension). By contrast, mere sensation, and the lower half of perception then, are more passive/responsive on the part of our consciousness; we must "wait upon" empirical objects to display themselves to us (though we can seek them out, to be sure, from the side of our practical reason no less) before we can have substantive knowledge about their local realities.
Now Kant also distinguishes a vaguely "positive"/"substantive" attempt to use the concept of noumena, from a negative/limitative use that can be successful where the substantive use cannot. And he says that, "Spacetime is (3+1)D," is synthetic, but he doesn't say that spacetime of alternative dimensionalities would be a matter of things-in-themselves. It would still be empirical (except insofar as our apprehension of space and time in themselves is a priori).
So, initially, I would think that the type from the second Critique is an idea of reason. More generally, I would think that Kant's use of the word "type" hearkens back to the technique of Christian typology, where it is not types/tokens or types/terms but types/antitypes, and an antitype is at once more general and more specific than its types (it is general enough to be the a priori reason for the types to be what they were, e.g. Joshua as a type of Jesus is by having features that generalize appropriately over the particularity of Christ, yet by being the standard of said generalization, the antitypic of Christ also serves for a generalization over the types as well).
The relationship between the type and the moral law in itself might then be construed as the variable of (N+M)D-spacetime. It (the type) is phrased in terms of laws of nature, and on Kant's account, nothing more transcendentally constitutes the laws of nature than do facts about space and time as such. The variable structure is not equivalent to the moral law, because the moral law can be represented in terms of absolute closure (see Kant's remarks about the term "absolute" in the Transcendental Dialectic), or then a constant value for those variables (as the zone of intellectual intuition, of things-in-themselves). The positive noumenal "realm" is one where "(N+M)D-spacetime" is to be written more like "VD-spacetime," where "V" is the symbol for the completed synthesis of infinity within intellectual intuition.
But is the representation of the variable term "(N+M)D-spacetime" an idea of reason proper, or more like a notio? Does it fall on the substantive or limitative sides of the internal distinction in the concept of noumena? Maybe you could say that it occupies a vague boundary within that very distinction, between the epistemic dilemma of its horns ("How do we know about things-in-themselves at all?").
EDIT: it must be important that he uncertainly talks about the type as a "scheme of a law," in that it must involve the transcendental imagination, yet over the idea of the moral law. It has to represent a functional interlude in the architectonic of reason, a higher-order fact about the relationship between the term "idea" and the term "type" and the transcendental role of the imagination in the theory of theoretical knowledge.