Metric Baumgartner Theorems and Universality

It is consistent with the axioms of set theory that for every metric space X which is isometric to some separable Banach space or to Urysohn’s universal separable metric space U the following holds: (?)X There exists a nowhere meager subspace of X of cardinality א1 and any two nowhere meager subsets of X of cardinality א1 are almost isometric to each other. As a corollary, it is consistent that the Continuum Hypothesis fails and the following hold: (1) There exists an almost-isometry ultrahomogeneous and universal element in the class of separable metric spaces of size א1. (2) For every separable Banach space X there exists an almost-isometry conditionally ultrahomogeneous and universal element in the class of subspaces of X size א1. (3) For every finite dimensional Banach space X, there is a unique universal element up to almost-isometry in the class of subspaces of X size א1.