Odd-degree Ext dimension conjecture for Auslander-Gorenstein Nakayama algebras

Let $A$ be an Auslander-Gorenstein Nakayama algebra, let $S$ be a simple $A$-module, and let $i$ be an odd integer. Odd-degree Ext dimension conjecture. One should have

$$\dim \operatorname{Ext}_A^i(S,A)\leq 1.$$

The conjecture would imply stronger homological properties for simple modules with odd grade in Auslander-Gorenstein Nakayama algebras. The surrounding discussion motivates it through the notion of $n$-regularity, but the source gives no resolution of the conjecture.