We dealt with this a lot in SAR, before UTM grids were printed on the available maps. We eventually did special edition maps with an arbitrary grid placed on them, so we could say, "I'm in grid A-1, upper left corner." Even so, you often would place yourself by saying, "I am right next to the "a" in canyon, etc. These days you could use UTM coordinates, if both parties understand the system.

Rather than giving bearings to the helicopter, I would recommend using a signal mirror (if not available almost any reflective surface) by day, and ideally a strobe light or fire at night. You don't need to be in contact with the chopper, and it is simple, obvious, direct, and workable over long distances. It has worked like a charm numerous times.