If you really want to go to Jiko (it's one of our favorites), it can be done but isn't easy. They do have a dress code which can make coming direct from the parks more difficult:
Men may wear khakis, slacks or dress shorts and collared shirts. Jeans may be worn if in good condition. Sport coats are optional.
Women may wear Capri pants, skirts, dresses or dress shorts. Jeans may be worn if in good condition.
Not permitted are tank tops, flip-flops, swimsuits, swimsuit cover-ups, hats for gentlemen, cut-offs, torn clothing and t-shirts with offensive language and/or graphics.
As stated, expect to spend 1 1/2 to 2 hours unless you are really rushed for time.
traveling from AK to AKL, if you take the bus, add at least 30 minutes to your time as you may miss the first bus. Uber is a good choice. If we have a car, we usually drive to and from the park.
I would vote for Tiffins at the park instead.