The rig seen on many canoes both large and small by early visitors to Tahiti and the nearby islands was an extraordinarily high aspect rig not seen elsewhere in Oceania. A curved spar runs along the aft edge of the sail.
Even offshore voyaging canoes used this rig. Cook's expedition was astonished by its windward ability. It did however have drawbacks in that it appears the whole rig would need to be raised and lowered like a windsurfer and I have no idea how it could be reefed.
My first experiment with this rig had it installed on one of my Ulua outriggers. I eliminated the spar on the aft edge and supported the upper section with fiberglass rod battens that fitted into curved pockets. Predictably it went well to weather and looked very cool.
Later I built a slightly different version for a 27' Tipairua double canoe. Rather than using the curved battens which were difficult to furl after lowering the sail, I used a gunter arrangement to support the upper section. This has been successfully in use for the past eighteen years.