Only one type of argument for God's existence?

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There is not a single proper argument for God's existence and if one is proposed without being absolutely obscure it won't be ontological.

I probably don't have a clue either way but am interested, do you mean why it would be so or why Kant would think so?

He did think that. Check out B635.

When I read his religious views, I came up with the impression that there cannot be a proof about the existence or non-existence of God because the universe in itself and the universe in our perception (scientific or not) cannot be the same thing. The universe in itself is an exact thing, but this exact thing (or the thing in itself) by no means is the same thing with the human perspective (scientific or not) of the universe. Since our human knowledge of the thing in itself is a kind of thesis or defense (viz. we can prove that there are reasons which justify our assertions about the universe, but we are far from claiming that we know the universe), it is impossible to say that this defense of this kind of knowledge can stand as a proof of whether God exist or does not. I gave up reading Kant's thoughts on religions and God long ago, in order to get some grasp of his ethics.... and hence I cannot be help in your research. But I guess you have to find out how Kant defines knowledge in order to understand all his metaphysics.

I think there is a profound point which has dropped out of the consideration of this argument, which is that in traditional philosophy, there was a sense of the inherent goodness or fullness of being. This was in turn grounded in the notion of the 'pleroma'. The 'pleroma' is the 'totality or fullness of the Divine'; this is the source of the saying 'nature abhors a vacuum'. Essentially this is getting at the idea that 'being is good' - that is, the very fact of there being an earth, creatures, the heavens, and the rest of it, is understood as a consequence of Creation which necessarily ensures that everything that possibly can exist, will exist, and is good. Being is therefore fruitful, a gift - recall Fortuna's overflowing 'horn of plenty' - whereas non-being or non-existence symbolises nothingness, deprivation, poverty or chaos.

In addition to this, traditional philosophy also discriminated between what is real and what (merely) exists - which is an iteration of the metaphysical distinction of 'appearance and reality'. In Platonist philosophies (and in Aristotle and Augustine), the intelligible domain is of a higher degree of reality than the sensible domain; sensible particulars are real only insofar as they're expressions or instantiations of an archetype or form. But this or that particular, and indeed worldly existence itself, isn't necessarily either good, or even totally real, in its own right; it only exists as a simulacrum or facsimile of the real form or Idea (which is something that only the wise know; knowing it is what earns them the designation 'wise'.) So in traditional philosophy, the degree to which something is good at all, is the degree of faithfulness or in some sense the 'proximity' it has to its actual archetype and the ground or source of Being. So the mere fact of its existence is not necessarily a good thing as one might have an accursed form of existence; but the possibility that it can exist at all, is a good thing, from this point of view.

Kant's argument that 'existence is not a predicate' is: to say of something that it exists, is not to add anything to it. It's something like a tautological expression. Whereas, I think that the original impulse behind the ontological argument, is that what really is, is not necessarily the same as something that merely exists. So, very roughly speaking, 'what really is', is necessarily good; whereas what exists is not necessarily good - might be, or it might not be, depending on a number of things because after all, individual beings are merely contingent - except for their 'intelligible soul' which is what about them that makes them good in the first place.

So by the time of Kant, I think this understanding has to all intents been forgotten or lost. It was present in early medieval philosophical theology, I think, but became eroded by various currents of thought in later medieval time; I think the idea of the nexus between what is real and what is good, or the ground of goodness, has been lost. I think, anyway. It's a deep question. I have discovered that there is a form of neo-Thomism that tries to incorporate Kantian insights, so am doing some more reading.

See http://lonergan.org/2017/03/31/reality-or-being-are-these-the-same/ for a sketchy blog post on whether reality and being can be distinguished.

See https://luminousdarkcloud.wordpress.com/2012/02/28/radical-orthodoxy-a-theological-vision/ for the first of a series of posts on 'radical orthodoxy' which explores the 'flattening' of the understanding of ontology in late Medieval Europe.