Agree with the above - if tiger-fishing is important, then you're quite limited to hunting in proximity to a water body containing tigers, particularly with a 5 day duration.
Not sure where Kevin gets the timing/dates from as I see no mention of dates?
Sept/Oct is a decent overlap between late hunting season and early tiger season.
Pongola area in SA is an option - some nice enough hunting areas and the Jozini dam is probably SA's prime tigerfishing location (albeit chalk and cheese from the Zambezi). Probably the easiest and cheapest to access. There are also some prime photo-safari destinations in that area (including some proper top dollar venues) and Kruger & surrounds is not too far from there either.
Maybe
@spike.t's operation in Zambia would cover both bases in one package? Don't recall if there are tigers in the waterways in his area?