Ironically, the property was likely sized via eminent domain, but that aside, and IANAL, Pruneyard might make the speech part of this protected.
https://en.wikipedia.org/wiki/Pruneyard_Shopping_Center_v._R...
https://en.wikipedia.org/wiki/Pruneyard_Shopping_Center_v._R...
Pruneyard and subsequent cases established that as long as private shopping centers encourage the public to freely congregate in a common area at their leisure, that area is treated as a public square and people can engage in speech protected by the state constitution. This activity is limited to the common area of the property, it doesn't apply to areas which may be open for the movement of people. Strip malls and free standing stores are exempt because they don't meet the standard.