No separation in Bayesian uniform-pricing approximation for quasi-regular buyers

Let asymmetric regular and quasi-regular buyers be compared using the revenue approximation of Bayesian Optimal Uniform Pricing to Bayesian Optimal Mechanism, with tight ratio denoted by $\calC_{{\sf BOM}}^{\textsf{Bayesian Optimal Uniform Pricing}}$. Bayesian Optimal Uniform Pricing separation conjecture. For asymmetric quasi-regular buyers, this tight ratio is the same as for asymmetric regular buyers, namely

$$\calC_{{\sf BOM}}^{\textsf{Bayesian Optimal Uniform Pricing}}\approx0.3817.$$

Thus the conjecture predicts no separation between regularity and quasi-regularity for this approximation problem; the stated regular-buyer bound is known, while the quasi-regular extension remains open.