It looks like your R&R study will depend upon a wide variety of factors. Versatile tools will have multiple R&R characteristics. Like process capability studies, the tolerance on any given characteristic will play a crucial role in the results.
Unique setups for each job will have their own R&R. If you have multiple operators, each of them will have an influence.
As you indicate, environment will have its affect as well. If it cannot be controlled, I would recommend that it be at least monitored for temperature and humidity. Chart and track the data for an overall indication of stability. If the device is sensitive to vibration, that should be considered as well.
Overall, assuming the volumes of various parts would make it worthwhile, I would recommend using some SPC charting to take a look at the gage, at the very least for tracking your environmental factors. From there, perhaps a two level study. At the first level, multiple operators using the same setup and at the second level, the operators each setting up and running their tests individually.
How in depth you care to go depends on the available time and budget available. These studies can be expensive in terms of time spent and materials "held up" for the course of the testing. Spend a good portion of your time planning what you want/need to do so that the testing portion can run smoothly and quickly.
Regards,