Evenness conjecture for the trivializing number of virtual shadows

Let $S$ be a virtual shadow, namely a diagram with classical precrossings and virtual crossings, and let $\text{tr}(S)$ be its trivializing number: the minimum number of precrossings that must be resolved as virtual to guarantee that every resolution of the remaining precrossings is the unknot.

Evenness conjecture. For every virtual shadow $S$, $\text{tr}(S)$ is even.

This is proposed as an extension of the preceding result on virtual shadows. The source supplies no proof or evidence resolving the conjecture.