I just did Kenya (including Masai Mara and Amboseli, which are on the border with Tanzania) with a Fuji 16-55 and 100-400 (APS-C, so 24-70 and 150-600ish equivalent). Those with more direct experience might say otherwise, but I think a 100-400 even on full frame would suffice, especially if you have a 500mm on another body. If the 100-400 went on your crop sensor body it'd be plenty, assuming Tanzania is similar to the Kenyan parks.