If I understand this correctly, there are 3 EB lanes approaching the intersection in question, EB Baseline and NB Stepping Stone. Lane 1, is a right turn only. This is where the existing bike lane starts, but it now shifts to the left as it approaches Stepping Stone to be part of the rightmost lane of the 2 lanes that passes Stepping Stone. On my pic looking west, I placed an arrow showing your direction of travel (east) and where I think the new bike lane is located.

I'd be in lane 2 (middle lane) of Baseline as it crosses 185th and approaches Stepping Stone and ignore the existing bike lane on the curb that approaches the island. Being in lane 2 allows autos in the right lane to make their right turn and without you crossing their path. And, those cars that forget to turn until the last moment to Stepping Stone from lane 2 will be approaching you from behind, versus crossing in front of you if you were in lane 1.

I think the biggest danger are autos coming NB on Stepping Stone merging into EB Baseline, versus the traffic from behind on EB Stepping Stone. See the black Acura in the picture.

I would not ride on the sidewalk here and try to ride through that island. That looks damn dangerous. It isn't even marked as a crosswalk.

I think that the new bike lane is in the best position in a bad intersection, but it should start at the light at 185th and the old one should be removed. I think the old bike lane is in a poor location, since it appears that it was never intended to help riders pass that island EB on Baseline.