Hawaii to the central Pacific is not uncommon - you basically
head through Kiribati and Tokelau towards
Samoa. Any further east will probably be too upwind. Your start time depends on not arriving during cyclone season - April departure is reasonable. Jimmy Cornell shows the
route in his world cruising routes book - get your hands on one of these
books. And check out noonsite.
Once you arrive in
Tonga or
Fiji your next decision is NZ or Australia? The easiest way between the two is via the
South Pacific, so make your decision before you leave the
South Pacific and don't plan for sailing from one to the next.
You will want to leave the South Pacific by the beginning of November - the longer you wait the less chance of a bad low coming out of the Tasman Sea, but not waiting so long that you get an early season low coming down from the NW.
Enjoy your time in the South Pacific islands - no need to rush further south.
Samoa,
Tonga,
Fiji,
Vanuatu and
New Caledonia can provide you with multiple seasons of cruising, in between cyclone seasons.
You will need to check the respective visa rules for spending more than 90 days in either NZ or Australia. NZ does allow temporary
import of your
boat for up to two years without much difficulty or cost.
Regarding working in other countries - you do realise that you are entering on tourist visas? Internet-based
work to your home country should be OK, but nothing local.