High-density mixing-time constant conjecture for asymmetric open exclusion

Consider the asymmetric simple exclusion process with open boundaries, with parameters $a,b,p$ satisfying the assumptions of the paper's two-sided asymmetric regime. For $\varepsilon\in(0,1)$, define the mixing time $t^N_{\mathrm{mix}}(\varepsilon)$ and set $\hat a:=\max(a,1)$. High-density mixing-time conjecture. In the high-density phase,

$$\lim_{N\to\infty}\frac{t^N_{\mathrm{mix}}(\varepsilon)}{N}=\frac{(b+1)\bigl(\hat a^2(2b-1)+\hat a(b-3)+b\bigr)}{(b-\hat a)(2p-1)}.$$

A similar statement is asserted for the low-density phase. The conjecture is motivated by hydrodynamic and shock-wave heuristics, but the supplied text gives no resolution.