Defect formulas for Chebyshev surfaces and threefolds

Let $\mathcal C(n,d)$ denote the Chebyshev hypersurface of degree $d$ in $\mathbb P^n$, and let $\mathcal N(n,d)$ be its set of nodes. For a finite node set $\mathcal N$, write $S_k(\mathcal N)$ for the degree-$k$ homogeneous polynomials restricted to $\mathcal N$ and $\operatorname{def} S_k(\mathcal N)$ for their defect. Defect-formula conjecture.

(i) If $\mathcal C(3,d)$ is the Chebyshev surface of even degree $d=2d_1$ in $\mathbb P^3$, then

$$\operatorname{def} S_{3d_1-4}(\mathcal N(3,d))=3(d_1-1).$$

(ii) If $\mathcal C(4,d)$ is the Chebyshev threefold of degree $d$ in $\mathbb P^4$, then

$$\operatorname{def} S_{2d-5}(\mathcal N(4,d))=\left\lfloor\frac{d-1}{2}\right\rfloor\left(3\left\lfloor\frac{d-1}{2}\right\rfloor-1\right).$$

These formulas are offered as a potentially infinite family of examples with large Alexander polynomials. The supplied text gives no proof or resolution status for either formula.