Realization conjecture for topological conformal dimension

For every $d \in[2,\infty]$, let $X$ be a metric space and denote its topological conformal dimension by $\dim_{tC}X$. Realization conjecture. For every $d\in[2,\infty]$ there is a metric space $X$ with

$$\dim_{tC}X=d.$$

The preceding product constructions provide partial evidence for an affirmative answer, including examples with fractional topological conformal dimension; the full realization of every value in $[2,\infty]$ remains open.