The official ZED rules state that the ticket can be used for travel in the same zone, there's nothing about lower/shorter zones, but it's reasonable for an airline to accept a DFW-HNL for LAX-HNL. But there are caveats, primarily regarding taxes. In other words, if the taxes for the new routing are different that what was ticketed then the airline can refuse to accept the coupon. Otherwise, they're out whatever taxes should have been collected.

Most taxes are departure taxes, there are very few countries that apply an arrival tax. Unfortunately for you, the US is one of them. This means that you ICNSYD would not work for ICNLAX or ICNSFO because HA will not have collected the apprppriate US arrival taxes on the ticket.

Note too that regardless of what the ZED rules say or even what the member airlines tell their agents, as with many things it's ultimately in the agent's hands to decide.