Perhaps the easiest alternative warm weather destination would be Hawaii. That is readily doable using Alaska miles.
This past year we did a trip which included NZ -- but used a combination of Hawaiaan and American miles to do it.
For us this was the 'big trip'. Used Hawaiian airlines miles from Phoenix to Honolulu - coach -- we could tolerate that.
Stayed there for 2+ days.
Using American Airlines miles we flew on Hawaiian AIrlines to Sydney -- overnighted at the airport hotel and continued to Cairns on Qantas -- that was 65K AA miles. Stayed 3+ days in Cairns
Then using Alaskan miles, we flew Qantas from Cairns to Melbourne and stayed there for a week.
The Qantas flights were business class.
Our plan was to use Qantas from Melbourne to Auckland (using AA miles) but they changed flight times and rather than awake way too early in the morning, we paid for Air New Zealand premium economy to Auckland.
We did a tour of NZ for two weeks. Then, using Hawaiian Air miles few business class AKL-HNL-KOA. We have a time share on the big island and stayed there for week.
Then we used AA miles to fly direct from KOA to PHX -- paid a few bucks for economy plus seating.
Yup -- 5 weeks -- "the big trip". It was easier to arrange flights from HNL to Australia and from AKL to KOA with miles and that broke up the overlong flights.
Speaking of overlong flights -- if you had infinite miles -- you could fly to AKL via Dubai in a first class/business class oddessy -- 225K miles one way. <smile>