Does anyone know if there is a way to move a group of individual cadastral parcels as a block? I do not wish to merge the parcels.
It sounds like you may want to try the Transform Parcels toolbar:
The Transform Parcels toolbar can be used to provisionally move a selection of parcels in the parcel fabric. For example, you can use the Transform Parcels toolbar to move parcels so that they line up with an underlying orthophoto. When transforming parcels, parcel points can be snapped to and linked to existing control points.
This allows you to select a group of parcels and move or scale them as you see fit, the result being something that looks good, but which is not necessarily accurate.
Note ESRI's note (emphasis is mine):
Note: You would use the Transform Parcels toolbar when adjusting parcels to a control network using the parcel fabric adjustment is not feasible because of poor data quality. With a good quality, survey-accurate fabric, the parcel fabric adjustment should be used to move or transform parcels to control.