@Philip Glass wrote a great post with sound advice.
less than $10k can get you a VERY high quality dangerous game magazine rifle. It is likely to get you an untrustworthy DG double rifle. Buy smart.
I'd add, there are a lot of nice 235gr loads out there for 375HH. If I had $6000-$10000 to spend on a gun and could only afford one gun, I'd buy a 375HH and use it not just in Africa, but in lieu of a .300WM or .338 for US hunting. One gun to rule them all with utter reliability is a great plan. (whether a DR in 375 Flanged, or magazine 375HH)
If you have plenty of rifles, just not a DG "stopping" rifle, then going with a big boy whether double rifle or magazine is a fine plan. I chose a double because I'm a terrible shot with rifles, but a pretty solid shot with side by side shotguns. My instincts and readiness with a break action, plus their reliability and speed of getting off two good shots made me a good contender for a DG double. Not everyone is the same, go with what you're going to know, trust, and use frequently.