The 4-adjacent Gray code conjecture for descent sequences in co-RGC order

A descent sequence is a restricted growth sequence defined analogously to an ascent sequence. List the set of length-$n$ descent sequences in the order $\prec_c$.

4-adjacent Gray code conjecture. The resulting list is a $4$-adjacent Gray code.

This conjecture concerns whether the co-RGC order has the bounded-adjacency Gray code property for descent sequences. It was checked by computer for $n\leq 10$; no general proof or disproof is given here.