Chad does not border Ethiopia. Sudan (Darfur) is inbetween and there you have your problem. Search the Hubb because there are many postings on crossing through Sudan/Darfur which I believe hasn't been done for years (by privateers). This is a war zone.
Crossing the CAR is possible but a hairy undertaking, CAR being in state of constant anargy. There are some Travellers report on this as well.
There is even a report of a Belgian car (radiobaobab) going from Zambia through DRC to Cameroon but I think that was not such a succes either, practically destroyed the car, flipping on its side due to concave roads up to 5 times a day! Not real fun. Search the Hubb, you will find the threads.
Crossing from west to east and vise versa has been a problem since 2002.
Your best bet is to continue all the way down in to Angola, then turn east towards Zambia and then up again if you need to go to Kenya.
That actualy was our initial plan too but once in Angola we continued to SA and decided to drive back home again along the east coast, was the best decision of the trip, you get to see it all!