The NA+ conjecture for random cluster measures with q<1

Let $G$ be a finite graph and consider a random cluster measure on its edge sets with parameter $q<1$. Random-cluster conjecture. Every such random cluster measure is NA+. Equivalently, the measures are NA. The conjecture would encompass uniform measures on forests, spanning trees, and connected subgraphs; a related NC+ statement was noted to be proved for series-parallel graphs.