How about start by eliminating per diem payments to the legislature? Move them all to Anchorage instead. Cheaper there, and no other state employees get paid per diem to go to their jobs. Eliminate their "we fly home every Friday and back on Monday" habit - they get one round-trip ticket per session if they're outside the local commute area. Eliminate staff travel - once they're in Anchorage there's plenty of local people available.

Once you do stuff like that, ask Revenue what kind of tax they can implement with no additional staff. It won't be much, I bet. Want an income tax? It'll end up being a flat tax (no staff to deal with anything more involved). Change the oil and business tax mess to be a flat 1% of all revenue, no deductions. (You just made it cheaper to pay the tax than try to avoid it.) Eliminate a bunch of staff attorneys, paralegals, etc. that do nothing but deal with oil taxes.