Small-trade conjecture for subsets of Latin squares

Let $L$ be a Latin square of order $n\geq 3$, and let $S$ be a subset of its entries with $|S|\leq \left\lfloor n^2/4\right\rfloor$. For a Latin trade $T$ in $L$, let $R(T)$, $C(T)$, and $E(T)$ denote respectively the numbers of rows, columns, and elements involved in $T$. Small-trade conjecture. There exists a Latin trade $T\subseteq L$ such that

$$T\cap S=\varnothing$$

and at least one of $R(T)\leq 3$, $C(T)\leq 3$, or $E(T)\leq 3$ holds. This conjecture is motivated by the use of small trades to rule out small uniquely completable or critical sets. It is stated as a conjecture in the paper; no resolution beyond the discussion and the verified order-seven case is supplied here.