a little quick research, and I think all but the lechwe are in Tanzania, with the Grant's gazelle only huntable in Tanzania and Ethiopia. Sitatunga and Lechwe are commonly hunted in Zambia together, and I would wager waterbuck and bushbuck could be added in zambia as well. I believe you can go on a 10 day trip to Maasiland Tanzania for the Grant's(and other plainsgame.) It looks like the most you could get in one single safari would be 4 out of 5. If money was not a concern, putting a Zambia trip back to back with a Tanzania trip would probably be the best way to get those 5 in the same trip.
The only other considerations are there are 2 species of Waterbuck, and multiple species of Bushbuck, so if the ranges of the ones you specifically want overlap or not could be a concern. If any waterbuck or any bushbuck would work my above plan would be the best bet.