Another option is to bring in a small cooler with a baggie of ice. Even labeling your ice tray will not keep people from using it.
When I lived in the dorms as an undergrad, someone not only stole my ice out of my clearly-labeld ice trays but they also stole my trays. I finally found them, weeks later, sitting in the sink in the communal kitchen, covered in cooking grease. Yeah, into the trash they went.
I later purchased a small lockable box to keep my stuff in.
This ^^^. OP, you might find more and more people appreciate you providing ice until it becomes your part-time job. Google "fridge locker" and lots of options come up at around 10$. I'm thinking of getting one for chocolate around here, it seem to "disappear" faster than is healthy for my kids (or DH
). Now, if someone steals your locker your workplace has bigger problems...