MacMahon's enumeration of all plane partions (PP) inside an $n$-cube generalizes to
$${\tt PP_n}(q)=\prod_{i,j,k=1}^n\frac{1-q^{i+j+k-1}}{1-q^{i+j+k-2}}.$$
A $q$-analogue of symmetric plane partitions in an $n$-cube
$${\tt SPP_n}(q)=\prod_{i,j=1}^n\frac{1-q^{i+j+n-1}}{1-q^{i+j+i-2}}.$$
The *ordinary* self-complementary plane partitions in a $(2n)$-cube
$${\tt SCPP_{2n}}=\prod_{i=1}^n \frac{(i-1)!^2 (i+2n-1)!^2}{(i+n-1)!^4}.$$
The following numerical observations fascinated me. Any explicit and pointed reference would be appreciated, if available.

QUESTION.Is there some sort of overarching explanation for these identities? Failing short of that, can you give a combinatorial or conceptual reason? $${\tt SPP_{2n}(-1)=PP_n(1)}, \qquad {\tt PP_{2n}(-1)=SCPP_{2n}}, \qquad {\tt PP_{2n}(-1)=[PP_n(1)]^2}.$$

I believe that ${\tt PP_{2n}(-1)=SCPP_{2n}}$ is known.