The rectangle poset and the action of rowmotion on it are two well studied objects in dynamical algebraic combinatorics, but work involving the trapezoid poset has proven more difficult. In 1983 Proctor showed that the number of reverse plane partitions of the rectangle poset and its associated trapezoid are the same. Since then it has been an open problem to find a bijection that is equivariant with respect to rowmotion. We give a birational map between labellings of these posets with positive real numbers that gives a bijection between these reverse plane partitions after tropicalization and restriction. We also give partial results about the equivariance of this map with respect to birational rowmotion.

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