Transience conjecture for unions of WUSFs on transitive transient graphs

Let $G$ be a transitive transient graph. For $\varepsilon>0$, let an $\varepsilon$-$\operatorname{WUSF}$ be obtained by independently retaining each edge of a wired uniform spanning forest with probability $\varepsilon$. Transience conjecture. On $G$, every connected component of the union of a wired uniform spanning forest and an independent $\varepsilon$-$\operatorname{WUSF}$ is almost surely transient. This extends the established behavior for transitive unimodular nonamenable graphs and is motivated by the expectation that unions of independent USFs are supercritical; the conjecture remains open in general.