Although Kant does not have the clearest account of some of these propositions in his system, I think he could have formulated them (if the question of their "existence" is posed) in an analytic way, for example in this case:
"There are synthetic a priori truths" = "If there are any truths, these are either analytic or synthetic"/"Every truth is analytic or synthetic"
Now as for individual synthetic a priori truths, the demonstration of their truth requires synthetic means, so in a sense they represent themselves as, "I am a synthetic a priori truth," and arriving at this representation will involve synthesizing their truth.
On the other hand, perhaps we might be able to prove by analysis first that some proposition S is not analytically true if it is true at all, but this will eventually also analytically lead to, "Therefore, S is synthetically a priori true if true at all." Again, discharging the conditional renders a proposition that can be construed ontologically, hence synthetically; but if framed as an existence question, we run into Kant's claim elsewhere that existence claims as such are the purview of experience: a priori we can decide a few vague possibilities and necessities too (vs. the categories of modality), but not absolutely possible or necessary existence itself. So the specific existence of a synthetic a priori truth might seem intuitive from the outside, but perhaps instead it is analytically a posteriori true that some synthetic a priori truth is as it is at all. Kant does not officially allow for analytic aposteriority, and his own anticipation of a Kripkesque semantics for water terms does not frame the empirical relativity of water as analytic; on the other hand, when Kant discusses the historically "famous" reference to "truth, unity, and goodness," he says:
Thus the criterion of the possibility of a conception (not of its object) is the definition of it, in which the unity of the conception, the truth of all that may be immediately deduced from it, and finally, the completeness of what has been thus deduced, constitute the requisites for the reproduction of the whole conception. Thus also, the criterion or test of an hypothesis is the intelligibility of the received principle of explanation, or its unity (without help from any subsidiary hypothesis) – the truth of our deductions from it (consistency with each other and with experience) – and lastly, the completeness of the principle of the explanation of these deductions, which refer to neither more nor less than what was admitted in the hypothesis, restoring analytically and a posteriori, what was cogitated synthetically and a priori [emphasis added].