Put a 3-way bridle on the sail, from the mast tip, the mast foot, and the clew, all meeting at the one spot.
Attach a line to this spot. Fly the sail like a kite.
When the sail reaches steady state (which will require some tweaking of bridle lengths, and will probably require someone holding it to stop it crashing) then look along the single line, and extend that line to the sail, past the bridle. It will hit your sail right where the COE is.
Edit: You may need to make up some form of support frame for the top bridle connection, which will make the mast tip bend away from the wind instead of towards the wind. I leave this as an excercise for the reader