"Clearly the Dividend would be funded at least in part by the income tax revenue."
You are stating that an income tax would fund the Dividend?  Source?  The AK Constitution provides that the only source of revenue for the PFD is "at least 25 percent of all mineral lease rentals, royalties, royalty sale proceeds, federal mineral revenue sharing payments and bonuses received by the State."  As to the PFD distributions those come only from the earned income on the PFD principle per statute.