Sawyer's extrapolation conjecture for mixed weak-type maximal estimates

Let $M$ be the Hardy–Littlewood maximal operator on $\mathbb{R}^n$, let $u$ be a weight in $A_1$, and let $v$ be a weight satisfying

$$\Big\|\frac{M(fv)}{v}\Big\|_{L^{1,\infty}(v)}\le c_v\|f\|_{L^1(v)}.$$

Sawyer's extrapolation conjecture. There is a finite constant $c$, depending on the $A_1$ constant of $u$ and on $c_v$, such that

$$\Big\|\frac{M(fv)}{v}\Big\|_{L^{1,\infty}(uv)}\le c\,\|f\|_{L^1(uv)}.$$

This conjecture proposes extrapolating a weak-type estimate for the weight $v$ to the mixed measure $uv$ whenever $u\in A_1$. The surrounding discussion gives positive and negative examples for related hypotheses, but the source does not state a resolution of this general assertion.