Wow Dave, what a challenge, I like a challenge! Good for you for taking on such an adventure. It's clear that you've already done heaps of research and your enthsiasm is almost contagious! Please email me your detailed itinerary, I'd be very interested.
I'm going to look into your specific questions and I'll get back to you as soon as I've got the most up to date info. However, please just bear in mind the following notes of caution for now.....
Firstly, Taking just 9 weeks to do this trip is probably going to be your biggest challenge, why do you want to pack so much in? or perhaps the mega tight schedule is the challenge!?
Secondly, taking 9 weeks with your own transport would be tricky but on public transport....................!! Just bear in mind that when someone tells you "the bus is coming soon" this means "the bus is coming in the next few days - if you're lucky", "the bus is coming now" translates as "the bus is coming today", and "the bus is coming now now" means the bus is coming in the next few hours".
This is not in anyway trying to discourage you, I just want you to be prepared!!
The part of your schedule that concerns me most is leg 3, it might be possible but you would see nothing, it would be constant, hard travelling, just bear that in mind. This kind of travelling is an experience in itself and one that I enjoy the experience of every now and then!
I think your budget is manageable, certainly food and accommodation you can get by on as little as $6-10usd per day. Transport costs vary wildly and hitchhiking will be the cheapest but will still cost you a negotiable fee in most cases. However, be prepared to pay more to leave quickly otherwise transport will generally leave only when full or almost full which might not fit your schedule.
Lake Tanganyika is still cause for concern in terms of security but again I'll get back to you once I've got the latest.
Whatever happens this is going to be a great adventure and I'm looking forward to hearing more.