Expert Flyer showing an AA fare ALG - HNL base fare of £977, books into D (the ALG to LGW into J if you go that way). May be possible to get 920 TPs out of that, including taxes total around £1380 so could be as low as 1.5p per tier point. Fare rule DNE0F6R5.
A quick search shows a Mercure hotel near the airport for about £80 per night. Good award availability on BA to position out ex LGW.