A Borel Ramsey theorem for strong similarity types of Fraïssé limits

Let $\mathcal{K}$ be a relational Fraïssé class with finitely many relations and a finite constraint set. Suppose that $\mathcal{K}$ satisfies the Ramsey property or has finite small Ramsey degrees. Let $\mathbb{K}$ be the Fraïssé limit of $\mathcal{K}$, equipped with a linear order on its universe of order type $\omega$. Strong similarity type conjecture. There is some notion of strong similarity type such that the collection of all subcopies of $\mathbb{K}$ having the same strong similarity type has the property that all Borel subsets are Ramsey.

This conjecture seeks an infinite-dimensional Ramsey theorem for broad classes of Fraïssé limits, extending the role of strong coding trees in the known results for the Rado graph and Henson graphs. The source presents it as a prospective direction and gives no resolution.