Once movement occurs does Unwedge continue to calculate the factor of safety based on the buoyant weight of the block?

The program does not assume that once there is movement there is a drop in water pressure and the factor of safety reverts to a dry case.  If there is water pressure, the factor of safety calculated always accounts for this pressure.

For more details on how the factor of safety is calculated with and without water pressure, see the Unwedge Factor of Safety Theory Manual.