Having been on safari several times,the last for my 80th birthday,I will give a personal answer.
Most car/vehicle hire firms WIll let to pick up and drop off in different towns or locations.
However,this WILL incur a drop off fee(to cover returning the vehicle to it's original depot).In most countries/cities that are in built up areas the fee is not TOO high.
However,given the distances that the vehicle may have to cover to return it to it's original site,this may incur a VERY high fee where you are intending to travel (if it is possible at all,as there may be no drop off site in the wilds of the bush!LOL)
I would recommend asking the relevant hire firm in the country you are intending to travel in.Only they can answer 100% your question.If you can find an email address you could do it that way.
Now regarding leaving a safar en route,you cannot do this for several reasons.
It would not only invalidate the travel companies insurance,they would also be held responsible if anything happens to you after you leave their care.
I know of one person who did this,and they now reside in a lions tummy!
It would aslo invalidate your travel insurance for the same reasons as above,(because your travel insurance assumes you are in the care of the travel company).
So overall the "leave a safari" idea is a bit of a non runner.
Hiring a vehicle is OK,but you would probably have to drop it off where you picked it up,due to there being very few hire care/vehicle offices outside of towns/cities.
and there are not many of those in the wilds of East Africa!
I hope this is helpful.