There are so many more freight companies that trying to chase down brand names like passenger airlines or UPS/Fedex may not be worth your time or your money. When I moved from Oregon to California earlier this year, I went to a Pakmail, and they took an apartment's worth of furniture (450 lbs), fit it onto two pallets, and booked it for me on Estes shipping for ~$550. That may sound a little pricey, but it was far less than the thousands of dollars that moving companies like United Van Lines were quoting. It may be different for Hawaii, but the Estes website says it does ship there.

My advice is to similarly go to a Pakmail or another good neighborhood shipping store that deals with all the freight companies. They will know the best solution for you.