As I am sure you have found, those timings just don't work with the scheduled flights.
As I see it your options are (i) coach (coaches leave up to 19:30 and at 06:00 and take up to 7 hours to central Lusaka, then a taxi from there); (ii) one-way car hire (7 hour drive); or (ii) if money is no object enquire about an air charter, there are a number of outfits at Lusaka who cater to the safari industry. Or (iv) change your schedule.
Good luck!