If you can add some logic to the control then a pretty clean solution can be made.
I don't know the control on your machine and the following is based on the assumption that the Cycle Start signal is a 24VDC momentary input to the control. This is typical of all CNC controls that I have worked on, but again, I don't know yours.
If you can't do the logic change, then dandrummerman's suggestion is a start, but needs another switch added.
The switch mounted to fixture needs NO and NC contacts. When the fixture is in the OP1 orientation, the switch should not be actuated. When the fixture is oriented for OP2 the switch should be actuated.
An additional switch with both NO and NC contacts needs to be mounted at some position where the machine can actuate it, but not its "normal" starting point.
When the first operation is ready to be run, the fixture will be in position 1 and the machine will be in its normal starting position. At this point, power will flow through the NC contacts of both the machine switch and the fixture switch and the machine Cycle Start switch can function to start the program. If the fixture is not in the OP1 position, power is interrupted and the cycle will not start.
Just before you temporarily pause the program, position the machine to actuate the machine mounted switch. The fixture is then moved to the OP2 orientation. Now power can flow through the NO contacts of both the fixture and machine position switches and the machine Cycle Start can function to start the continuation of the program. If the fixture did not get positioned to the OP2 orientation, then power is interrupted and the the cycle will not continue.
Hope that made sense. Sorry for the schematic being folded. I thought it might end up too wide to view as an attachment so I drew it folded. Turns out I did not need to. If it is confusing, let me know and I'll re-draw it unfolded and post again.
As with most things it is not foolproof as fools get smarter all the time. Nor is it failure proof. It will catch a lapse in operator memory though.