Near transversals in Latin arrays

An $m\times n$ array is Latin if each symbol occurs at most once in every row and at most once in every column. A near transversal of an $n\times n$ array is a partial transversal of length $n-1$, namely $n-1$ entries in distinct rows and columns containing distinct symbols.

Near-transversal conjecture for Latin arrays. Every Latin array contains a near transversal.

The source presents this as a plausible strengthening of the near-transversal conjecture for Latin squares. It notes that all Latin arrays have near transversals in the small orders treated by the paper, while the general statement remains open.