This is a partial answer...perhaps someone will improve on it!
Historically, most of the q-analog $q$-analog formulae (beginning from Euler) were derived based on the assumption that |q|$|q|< 1 1$ (to ensure series convergence) or $q=p^k$. q=p^k$ for a prime $p$. John Baez in one of his weekly finds (week184) discusses the geometric interpretation of q=1 $q=1$ (counting over $CP^n$), q=-1 \mathbb CP^n$), $q=-1$ (counting over $RP^n$) \mathbb RP^n$) and q=prime $q=$a prime power (counting over PG($F_q.$))PG($\mathbb F_q$)). There is no discussion for other values of q.$q$.
However, in Gasper and Rahman's Basic Hypergeometric Series, there is an inversion identity on page 4 which can be used when |q| $|q| > 1. 1$:
$(a; q)_n = (a^{-1}; p)_n (-a)^n p^{n/2p^{-n(n-1)/2} $ where $p=1/q$.
This returns a new expression in base |$\frac{1}{q}$| $|1/q| < 11$. You can see some examples of the identity being applied in Gasper's Lecture Notes on q-series (Exercise 1.1, Exercise 2.3, pg 14)
I have no idea how to interpret the result geometrically. Could it be relevant to Buildings, Buekenhout geometry or p-adic $p$-adic geometry??
