Allocation conjecture for wide Young diagrams

Let $Y$ be a Young diagram, and let an allocation mean a coarse filling obtained by subdividing $Y$ into subrectangles and partitioning the symbol set into smaller subsets, with prescribed counts of symbols from each subset in each subrectangle. Let $Y$ be wide when every subdiagram formed by a subset of its rows dominates its conjugate. Allocation conjecture. Every wide Young diagram has an allocation. By the theorem cited in the paper, having an allocation is equivalent to being Latin, so this is an equivalent reformulation of the Wide Partition Conjecture. The paper proves the corresponding Latin conjecture for three distinct row lengths, but the general allocation assertion remains open.