Acetone/DMSO/NMP and the like are pretty good removers for usual novolak based resists. So is oxygen plasma, but that might also oxidize surrounding materials.
For most novolak based resists, you'll need an alkaline developer. If ZnO succumbs to that, then you have 2 options:
reduce concentration until it doesn't etch ZnO. You'll have to try this. TMAH can be better or worse than inorganic solutions.
deposit or spincoat a protective layer underneath the novolak, that is not harmed by alkaline solvents. Develop novolak. Etch through the protective layer with a second agent, that does not harm ZnO.
Upon slight further reading, it looks like ZnO is stable neither in acids nor bases. So you could spincoat a very thin polymeric layer underneath the photoresist, crosslink it, develop the mask above, then use oxygen plasma to etch through the crosslinked layer. The plasma will also remove a corresponding thickness from the photoresist, so that should be thick enough.
And a separate option would be of course, to prepare your gold electrodes not via a lift-off process, but by etching itself. I.e. deposit gold, make a negative mask on top of gold, and use dry etching to remove gold.