Type B distributional identity for oriented swap absorption times

Let $T_0,\dots,T_{n-1}$ be the absorption times in the type $B$ oriented swap process, and let $L((0,0),(u,v))$ denote the corresponding half-space LPP passage time. Type B distributional identity conjecture. One has the distributional identity

$$(T_0,\dotsc,T_{n-1})\overset{(d)}{=}(L((0,0),(n-1,n-1)),\dotsc,L((0,0),(2n-2,0))).$$

This is the type $B$ analogue of a type $A$ identity that was originally conjectured by Barraquand, Corwin, Gorin, and Ruzza and recently proved by Zhang. The type $B$ identity remains open in the supplied source.