Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties

Let T be a compact, metrisable and strongly countable-dimensional topological space. Let MT be the set of all metrics d on T compatible with its topology, and equip MT with the topology of uniform convergence, where the metrics are regarded as functions on T². We prove that the set AT,1 of metrics dT for which the Lipschitz-free space F(T,d) has the metric approximation property is residual in MT.