Thanks, eyecue. I hadn't considered the effect of the xrays for being in checked vs. carryon. I definitely do not want to risk any problems with how they function.
These instruments are not super-expensive but they are mission-critical for this trip and it will be safest to just get them in my carryon. They need to be there when I'm there, or I'll have nothing to do.
I'm definitely going to FedEx them back to save space in my bag on the way back - my husband wants some sort of present from Austria and that will free up some room.