Pairwise disjoint Gδ witnesses in the countable-dimensional setting

Determine whether the results asserting that every finite-dimensional Borel space is o-homogeneous with pairwise disjoint Gδ witnesses (Theorem 6.2) and, assuming AD, that every finite-dimensional space is o-homogeneous with pairwise disjoint Gδ witnesses (Theorem 6.3), extend to all countable-dimensional separable metrizable spaces, i.e., whether the pairwise disjoint Gδ witnesses can still be obtained without increasing complexity.

Background

By the Gδ-Enlargement Theorem, a countable-dimensional space can be written as a countable union of zero-dimensional Gδ subspaces, which immediately extends the finite-dimensional analytic o-homogeneity result (Theorem 6.1) to the countable-dimensional context.

However, for the pairwise disjoint Gδ witness results (Theorems 6.2 and 6.3), the authors explicitly state uncertainty about preserving both pairwise disjointness and the Gδ complexity when moving from finite-dimensional to countable-dimensional spaces, motivating Question 8.2.