Add a reference plane in your model instead and dimension to the plane. That plane won't show up in your drawing view.
Sample below shows reference point in drawing. Same principle
Make a reference point with 1DOF and specify your base value i.e. 1000 then hide the 0 and the base value dimensions.
All your running dimension will look as if the start at 1000+
Base at 1000
Base modified to 500
Adding a plane seems to be a smart solution,
But I think Solid works should do something to update the dimension if overridden in the property manager at least for ordinate dimensions