I cannot comment on the adjust robtargets function, but what I can say is that wobj0 is a zero offset frame and is a default setting in the robot system and i believe it cannot be modified. Therefore, your robot program is not related to any frame at all and only relative to the robot itself. How will you calculate the new frame then??
The preferred way to do this is to use a measured TCP and choose 3 reference points around the fixture which would then define an origin point and the X, Y and Z direction of the workobject. Document where the points are and how the workobject was defined. All the robtargets would then be taught using that workobject.
When you move the machine to it's new location, the programmer or technician would redefine the workobject using the method as you have documented and then all of the robtargets will work.
If you have not yet moved the machine, I would recomment doing this and use the robtarget adjust feature to bring your robtargets in line with the new workobject. Don't forget to document how you meassured the workobject.
I hope this helps, good luck.