Pietersburg-Livingstone-Lubumbashi-Kinshasa may work if you don't have much range. Need to check on that. Not much problem overflying Zim but you must get a clearance, as for all others, and keep it on you. Only real problem is the Zimboon controllers getting bored and asking you for radial and distance from arbitrary VORs every three minutes.
Watch out for CBs around Bulawayo.