OK, so I saw the concept plan, and I don't really see any issue.
I highlighted two different paths. If you stay on the road (red line) you can continue to legally use the road crossing Broadway on Lincoln. But if you follow the green line, you would already be on that light beige area, the "promenade", and would cross on the north side of the road using the sharrows, and then continue on the "cycle track" on the north side of Lincoln. If you notice, the promenade is a pedestrian-only area, with trees and plantings, and Lincoln is now a one-way street (east). Also, the cycle track east of Broadway on Lincoln is separated by a planted area, which is a physical barrier between bikes and vehicular traffic. The only issue would be the one you describe, where you are on the road west of Broadway, then try and transition to the cycle track on the north side of Lincoln east of the Broadway intersection. Even in that situation, you could turn left from the road through the intersection onto the cycle track at the northeast corner of the intx, but since it's probably an unprotected left, that might be a bit dicey. However, if you are coming from Main St, I would probably just turn onto the promenade on the north side of Lincoln, and ride the whole way following the green line. There's no reason why you'd have to be on the road on Lincoln between Main and Broadway, unless you aren't planning on continuing toward the IHT. Overall, it doesn't appear to be that bad a concept, TBH.