A plane partition, whose 3D Young diagram is made of unit cubes, can be approximated by a "coarser" plane partition, made of cubes of side length 2. We relate this coursening operation to the squish map, which is a measure-preserving map between the dimer model on the honeycomb graph, and the SL_2 double dimer model on a coarser honeycomb graph. This allows us to re-use existing computations of the 2-periodic single-dimer partition function (and, in principle, the correlation functions) in a portion of the parameter space of the harder double-dimer model. The other direction of the map allows for some interesting conjectures in plane partition enumeration, when some of the generating function variables are specialized to roots of unity.