Indeed.
As you have pointed out, the pertinent issue is increasing the number of leasable parking spots for Slate, so they can retain tenants at the Blue Cross Centre, and to keep their options open for future expansion of the Blue Cross Centre. The issue has less to do with general public parking, but it would seem reasonable to try and increase parking intensity in any structure which is built by making the facility available to public parking in the evenings and on the weekends.
As you pointed out in your graphic, the eventual redevelopment of Downing Street (with enclosed parking), and the construction of a parking garage on the land south of the Marriott should solve the situation.
I would hope that the development of the land south of the Marriott would be multipurpose, including additional office space for Slate to lease out, as well as street front retail/commercial store frontage along Assumption to try and improve vibrancy of the area.