Random Steiner quasigroup row-cycle and subsystem conjecture

Let $S$ be a Steiner quasigroup of order $n$ selected uniformly at random. Let $\ell(S)$ be the length of its longest row cycle, and let $m(S)$ be the size of its largest proper Steiner subsystem. Random Steiner quasigroup conjecture. With probability $1-o(1)$,

$$\ell(S)>m(S).$$

If true, this structural property would yield average-case polynomial-time canonical labelling, and hence isomorphism testing, for Steiner triple systems. The source presents it as a belief and gives no evidence of a resolution, so it remains open.