That's one of those personal questions that only you can really answer. I think that 300mm is rather long (even without the TC) for the Safari ride. It bounces and moves so much that it would be hard to get a good shot with a lens that long.
As for the trails, I suppose that it would be nice in spots, but that's an awfully limited use for such a heavy lens to carry all day.
It could be handy for closeups at the shows. It's a bit slow for the FotLK, but could work with a high ISO at Nemo. It would be great at the bird show. I haven't been able to sit through the Pocahontas show, so I couldn't really comment on it's use there.
I lug a 70-200 f/2.8 lens around the AK whenever I go and I find it worth carrying, so I'm no wimp on hauling camera gear. Still, I don't think I'd take a 300mm f/4 with me. I just don't think I'd get enough use to justify the weight/bulk all day.
Different strokes for different folks though. You might be able to snag some of the best gorilla shots any of us have ever seen and you'd think it was all worthwhile.