At least one of their UHV should link to culture. Let their UB have unlimited artists, and/or let their UP enable converting culture to hammer or settler. Or this: no city number maintainence cost under tribalism or city states.
Starting date: 600 AD
Starting Techs: Fishing, Sailing, The Wheel, Hunting, Mysticism
UP: Power of Island Nations: Double culture and no city maintenance cost under tribalism.
UB: Moai: Requires Masonry, double build speed with stone, replaces Lighthouse, +1

per seafood resource and/or tile, +1 priest(or artist/engineer?) slot, +2

(no bonus health or trade)
UU: Canoe: as OP suggests
UHV:
1. Control New Zealand, Hawaii and Easter Island by 1200 AD. Very good, historical goal Locutus, perfect date too.
2. Build 10 Moai by 1400 AD. Would require colonization of most of stability map, or more.
3. 50000 culture in/by 1850 AD. Would require player to resist any European or Asian incursions and remain in tribalism to maintain culture levels and allow for isolated, peaceful building.
If you give Easter Island a stone resource, these changes give Polynesia more realistic production and goals, and better represents their decentralized society and actual achievements, and because of the nature of the UHV and UB, the player will be encouraged to settle near seafood and fight Europeans anyways. More is incorporated!
Perhaps we should just make the UU replace Caravel altogether. Make it require Mathematics/Construction instead of Optics, etc.
No, it should replace Galleys. We don't want Polynesia to have Galleys, Triremes or Caravels unless it does ahistorically well, so if Canoes replace Galleys, all they should have is Canoes. Why would we want Polynesia to be able to conquer anyone? Without the use of a military for most of its existence, Polynesia becomes a very unique civ.
EDIT: If Polynesia is too strong even with these changes, the Moai could replace Harbors instead, and thus get rid of the +1 food and seriously nerf them.