The Issue
The report states that the underground passageway is on a track that will dead-end into the underside of the existing Grand Staircase. There are more details in this article from the Broadsheet which highlights the issues, including some very savvy positions that support retaining the Grand Staircase.
I believe that a compromise can probably be worked out, and there may be multiple solutions that would work. To that end, I am submitting my own idea that would compromise by saving at least 50% of the Grand Staircase and provide a flow around it that aligns with the current architecture and decor:
One Solution
If you consider the staircase that faces the Hudson River, and envision two opposite wedges on the portions that have the hand railings that are furthest from the River, and a larger central wedge; the two smaller wedges could be excavated to construct an inverted or collapsed matching portion that connects to the underground passage, preserving the central portion as is (instead of eliminating the entire stairway). The inverted (or collapsed) sections could use existing materials from the excavated portions to preserve the look & feel of the site. The center portion of the steps would remain for a dual purpose: access to the upper level, and "stadium seating" for performances in the Winter Garden".
The Team that calculates traffic flow can determine the appropriate angles/size of the portions for the two wedges that will achieve an optimum balance between traffic flow and aesthetics...
Here is a rough rendering of this idea:
This depiction focuses on the southern side of the Grand Staircase, where a portion has been excavated to allow for the "collapsing" or inversion of the steps to provide access up from the lower level where the passageway connects from the Transportation Hub.
The original marble would be reused to preserve the decor and continuity.