  R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are
two distinct bijections between the reverse plane partitions of a fixed
partition shape and multisets of rim-hooks of the same partition shape. It is
known that Hillman-Grassl may be equivalently defined using the
Robinson-Schensted-Knuth correspondence, and we show the analogous result for
Sulzgruber's insertion. We refer to our description of Sulzgruber's insertion
as diagonal RSK. As a consequence of this equivalence, we show that
Sulzgruber's map from multisets of rim hooks to reverse plane partitions can be
expressed in terms of Greene-Kleitman invariants.
