You might have a peek at this somewhat related thread: http://www.flyertalk.com/forum/showthread.php?t=723338

I think reach is really key. If I were to go on another safari, I'd probably seek to rent something like the Nikkor 200-400mm f/4G AF-S VR and maybe an even longer exotic prime like the 500 or 600.

That rental price sounds really, really high. If you are going to be in the U.S., you can buy the Nikon 70-300mm f/4.5-5.6G AF-S VR for about USD $500!

As a side note, depending on where you plan to buy the 18-200, be aware that this lens is hard to get, and probably not going to be in stock very often for you to just pick up at any store. If you know which shop you are going to buy it from, I would call them NOW to see if they have it stock, and if not, have them pre-order it for you to pick up when you get to the U.S. This lens can take months to come in, so you may be out of luck, to be honest.