Equality between gem-complexity and Matveev complexity for lens spaces

Let $L(p,q)$ be a lens space, let $k(L(p,q))$ denote its gem-complexity, and let $c(L(p,q))$ denote its Matveev complexity.

Lens-space complexity equality conjecture. For every $p\ge 3$,

$$k(L(p,q))=5+2\cdot c(L(p,q)).$$

The claim is suggested by propositions in the paper and by equality in specified infinite classes; the supplied text gives no resolution status.