I suspect you will have great difficulty getting one shipping company to do it all for you from home.
Panama south isn't particularly difficult, Girag or Challenge Air isn't a problem, to Quito, or Bogota.
Flying to NZ you should be able to prebook, but I would recommend against it. Too much pressure on a specific date, takes all the fun out of it. You may find yourself early or late because you have found things along the way that you thought were intersting and weren't or vice versa!
Flexibility is critical in my mind. If you aren't flexible in EVERYTHING you will not enjoy the trip.
Why one month in NZ and skip Australia? Perhaps save them both for another trip, and save a lot of money and time too.
West Africa is generally difficult, and expecting to book anything in advance or do anything quickly might be a little optimistic! The worst of it is that you may well be promised something, but 99.9% of the time it reflects what they would LIKE to happen, but has never and will never happen.
Again, be flexible. Allow lots of time. Plan on a day at any border, and three days in or out by air. You may well do it in less, and South africa and B.Aires are generally very easy to do in half day or less, but Panama and Quito 2-3 days. Egypt 3 days is normal flying out. Tunisia by land or sea is easy, air longer.
A suggestion would be to fly to Cape Town, use South African airways or Malaysia Air (cheaper) and do Southern Africa. A good intro to Africa and a lot easier, especially the logistics part. Also safer and lots to see.
Good luck, keep in touch, and let us know how you go.
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