Yes. As a Zambian Operator I think George has the best idea. Hire an aircraft from RSA and go from there. But get one of the Professional Companies in RSA to get your clearances. Whoever you hire from will give you the contacts. You will also need extra excess insurance.
Steer clear of Zim, mainly due to the fuel problem.
Yes you are right on your geography.
Vic Falls Town is in Zim. Livingstone in Zambia, but the actual Victoria Falls links the two towns with a spectacular bridge,border post linking the two.