I think the previous posters got it mostly right. I think you're seeing a combination of camera shake induced fuzziness and lens softness. You have to really scrutinise the pictures looking at the shutter speed / f.l. used to form an opinion about which is the prevailing trait in each one.
Additionally, one cannot exclude minor focusing errors with the slowish AF resuting from the lens+TC combo especially under not so bright conditions.
Shooting the 70-200 at max. focal length, max aperture with the TC20E is not a good idea anyway. If you want light the 80-400 is a much better proposition even with its slow AF.
Another idea is to back off your focal length (maybe using the 1.4 or 1.7 TC) and crop a bit more.
For stabilising the lens a beanbag or similar support is a better idea. Also, with the D200, up your ISO up to 800 to try and use shutter speeds higher than 1/60 at these long focal lengths.
Keep your VR on at speeds lower than 1/500 or so when using either a bean bag or a monopod.
Machine-gunning a sequence to select the best photo in post is also a good recommendation in such iffy situations.
Having said all this, the best lens for a safari IMO is the 200-400 lens. There's a reason people are paying lots of money for super teles... If you expect to regularly shoot under similar conditions, invest in that lens before upgrading your camera. If you upgrade to a D300 you will be gaining max 1 stop in terms of noise (and probably nothing that you cannot handle with the D200 and some post-processing). If you go the D3 way you will find yourself even more strained for reach and maybe short of cash to get a decent lens