If you have safety concerns I would agree with your idea to drop Libya, Egypt and Morrocco. Be very careful on where in Thailand, Malaysia, Vietnam, Brazil and Cambodia you visit. All of the above have terrorist, bandit or high crime rate issues.
I took 3 months off at the end of last year to travel and watch the rugby world cup. My tour was a week in Cape Town, 10 days in Perth, a week in Melbourne, a week in Brisbane, a weeks scuba dive course (3 days of which on a boat on the great barrier reef) 10 days in Sydney ( almost all rugby and drinking

LOL) yeah we won

. A week in Hawaii, week in San Diego and 3 weeks in Florida. If I was to plan again ( not around rugby) I would change a few things about .
If you're planning a tester trip to Asia, I would take in Asia in one trip and the other things in another. IMHO Safaris in the future are going to become more difficult to do properly. I feel we will lose the ability to see Africa as it was before it become developed. I don't think it's something that can be put off for a later date JMHO.
Considering the individual cost of flights to South Africa being quite high you can add it into a "round the world" itinerary quite cheaply so I would add it into a plan. I would visit/base myself in Cape Town as this is probably the safest place to visit in Southern Africa and there is a lot to see and do here. I would say spend a week to 10 days in Cape town itself and look to book a separate trip for a safari from Cape Town. They will do flights direct into the game reserve areas futher north. I believe Botswana is the best area for seeing game these days. IMHO the safari aspect of this trip is the one area I wouldn't look to do cut price. For safety and quality of experience it's worth paying top $$. You don't really need a car in Cape town and there are a lot of trips that are better done through a tour guide. I can give you some local TA websites if you're interested.
You can then fly direct from South Africa to Perth in Western Australia. I really liked Perth/Freemantle and Western Australia is a fantastic place to explore. Perth itself has an excellent public transport system and there's no need for a car here, if you wanted to Explore WA more it's a huge area and a car is definately needed.
On the East coast of Aussie I wasn't much impressed with Melbourne, but the penguin parade at Philip Island ( 2 hours south of Melbourne) was one of the highlights of the trip. Sydney was mostly rugby and passed by in a blur, but I really liked the bits I remember

and it's a must on a tour. I then rented a car and drove up to Brisbane (about 600 miles). I stopped at Coff's harbour on the way up and there are some beautiful spots in this area (Port Macquarie and Boambee). Brisbane is a great city and close to a number of themeparks and Steve Irwin's (Croc hunter) Zoo Australia that I thought was an excellent day trip. I did my dive course at Bundeberg
http://www.saltys.com.au/welcome.htm and I thought it was excellent value and a great trip. For people not wanting to scuba then you could easily continue the drive up to Cairns and the Gt Barrier Reef.
I wanted to include NZ, but the flights on to Hawaii made that difficult. On a trip for less than 3 months I would say you're better concentrating on less places and spending more time at each location. Otherwise you end up wasting so much time travelling.
I'd spend at least a couple of weeks in Hawaii, one week in Honolulu and exploring that Island and 1-2 weeks exploring some of the smaller islands.
West Coast I would probably book flights into and out of either LA or San Fran on the main "round the world" ticket and organise flights to other places I wanted to visit ( Canada, Mexico etc) separately. It's likely to be cheaper and offer you better flexibility to do so.
East Coast I'm sure you know reasonably well.
Even on that simplified tour plan I'd say one needs 3 weeks in Africa, 6 weeks in Australia and 5-6 weeks in the USA. If you have more time to fit in other destinations then that's fine, but having done a round the world in 7 weeks, even with limited number of stops it was too much travelling and not enough time at each place. I wouldn't consider spending less than a week in any destination, you lose a day on the way in, a day on the way out and it takes at least 2 days to orientate yourself, leaving only 3 days to get the benefit of a destination.