I may have mentioned this before, but I find that the "stay right" command is used when we as drivers actually would expect to hear a "turn right" even for the "pre-right-turn-cutoff-lanes" such as this one in your area. I have tried, and with pretty good success in many places, implemented a small work around which gives a turn instruction but still looks like a "cutoff lane." One such example is this one. Notice that on zoom-out, and in the client, the small kink to make a right-hand turn is barely visible.
Also, in the previous permalink you provided, there are incorrect turn restrictions enabled at both the beginning and end of all these segments. It looks like you overused the 'w' key. And if you're doing it there, then you are likely doing it in other places. 'W' should be used very lightly in situations involving 1-way segments especially. It does truly enable ALL TURNS, which is often what you do not want in these situations.

Area Manager North East PA
thank youuuuuu