In additional to the external & internal policy roles you could also consider government / ministerial relations roles within government agencies.
I would expect most advisor roles for experienced staff within (central) government would pay above $70k. A higher salary (particularly for policy or ministerial roles) would also be possible. To get the initial role and become familiar with the NZ 'Machinery of Government' may require starting at the lower end of the range, though with your background opportunities to move to more senior roles could be possible in the short to medium term.
Shawn