I probably spend around 6 to 8 weeks a year on Safari in Africa, so getting gear around has become a bit if an Art.
You mention a Hiking/Tent type Safari, so that may mean your Photography may well be mostly from Foot, as against from a vehicle, and that would suggest two different Rigs, or one Rig that would suit both Foot & Vehicle Photography.
Serengeti/Tanzania can be wide open plains, subjects next to the vehicle, or quite a distance away, if on foot I'de suggest mainly at a distance, which is where you want them if your on Foot, you don't want a Fully grown Male Lion 10 metres away.
A general purpose set up that you need to consider carrying in a backpack while hiking might look like this.
24-70f/2.8 L II
70-300 f/4-5.6 L
I'de suggest the 70-200f/2.8 L II + 1.4x as an alternative to the 70-300, but be aware the 70-200 f/2.8 gets quite heavy after a while, where the 70-300 is quite a bit lighter, the 24-70f/2.8 or the 24-70f/4 will take care of your wide angle & closer up Imaging, I'de go the f/2.8 here as you will then have something that will take care of those Dawn/Dusk shots.
The 1Dx might be an alternative to the 5DMKIII, but it's heavy and the real world value is better dust protection & 14fps over the 5DMKIII. I've used both in Africa and no issues with either. The 6d might be a choice as well, you loose the wonderful AF Options of the 5DMKIII/1Dx though, and generally I only recommend gear I own & use, but my Son uses a 6D + 28-300 when he comes with me & produces some great Images with this Combo.
This suggested gear will present no issues for Carry On, I had a horrible experience with Carry On gear leaving Dar Es Salam on a SAA flight, it finally worked out, but the Cabin Staff were removing carry on Camera gear at the door, even from Business Class Passengers, tagging and putting the gear to the Hold, in many cases unlocked, and despite Passengers being really upset, in a case like this you are best to refuse to Board and make them remove your checked baggage then get another flight.
Be also aware that any Camera Gear that you put into checked luggage stands a reasonable chance of going missing, out of Johannesburg is unfortunately infamous for this.
Otherwise, enjoy your trip to Tanzania, I was there for 5 weeks in June/July 2013 & totally loved it, except for Dar.