Well, you do have a couple of options. You could get a 70-200/2.8L used, or look at the sigma equivalent. I love my L, and I got it as a refurb for $899. If you do get the 70-200, you are going to need to get a 1.4TC to get more length on safari.
You could also try the 2 lens route - the 70-300IS for the safari and 85/1.8 for indoor sports. The 85 is the de facto basketball lens, as well as performances when you are within the first 10 to 15 rows. The 70-300 has excellent optics and IS to help you with long lens technique (you probably won't have time to fool with a tripod in the back of a jeep). It doesn't have "L" build, but it is rugged enough.
Or, you could go with the "buy now for safari, sell, and get an indoor sports lens later" strategy. I've not used the sigma 50-500 (aka BIGMA), but it might be worth looking at for the safari and getting something else for the indoor sports.
Current: 5DM3, 6D, 8mm fish, 24-105/4IS, 35/2IS, 70-200/2.8IS, 85/1.8, 100-400/IS v1, lensbaby composer with edge 80, 580's and AB800's
Formerly: 80D, 7D, 300D, 5D, 5DM2, 20D, 50D, 1DM2, 17-55IS, 24-70/2.8, 28-135IS, 40/2.8, 50/1.8, 50/1.4, 70-200/4IS, 70-300IS, 70-200/2.8, 100 macro, 400/5.6, tammy 17-50 and 28-75, sigma 50 macro & 100-300