I have hunted with Guav Johnson, a Zimbabwean PH, for Bongo in Cameroon. He also hunts Lord Derby, in both cases for Mayo Oldiri Safaris. He is one of the best PH's I have hunted with, and I intend to go back and get the LDE with him in the next few years (when I arrived in the jungle, I ran into Jim Shockey who was leaving on the plane that brought me in and he told me Guav was "one of the top 3 PH's" he'd hunted with). Not 100% on Mayo Oldiri, though they are fine, just not great, but they have some excellent concessions and in my view you go for the PH.
As for the gun, I'd listen to the PH you will be hunting with, but if I had a choice - and you didn't say this was one of yours - I'd go for a .375 H&H. It may not be jungle in LDE country, but the bush is pretty thick, and you want a bullet that can handle some brush. I'd find the .300 a bit light, but not inadequate if you had to bring it. Equally, the .416 is a bit heavy - you'll be carrying it for long days in high heat - and is more power than you need, and perhaps not quite the flat trajectory at the distances you'll probably be shooting at. But if I had to take one, it would the .416. Just my opinion.