Although I usually use a full-frame DSLR rather than a crop sensor (and a Canon rather than a Nikon), the following points might still be worth thinking about, alongside the other advice already given. Of course, these are just based on my own experience and requirements - your mileage may vary.
When researching an all-round lens for zoo work (previously I used a 70-200mm), I did consider a 150-600mm zoom for my Canon 5D (the field of view range would equate to that of a 100-400mm lens on your D7100). However, I abandoned that idea due to:
- weight of the lens/camera combo. I just knew that I would not enjoy carrying that weight around on an all-day zoo visit, and it would end up getting left in the car, or at home. I would also have wanted to use a monopod for support, at least at the longer end -- this would increase the weight even more. I'm not a bodybuilder, so I needed to factor the weight in.
- the minimum focus on lenses of this range tends to be approaching 3 metres / 10 feet. Many zoo enclosures are barely that depth in total, so instantly you've limited yourself in what you can photograph. You may be able to move backwards to compensate, but you often then run into problems with any mesh/fence (between the subject and the camera) coming more into focus and thus becoming a distraction, or reflections becoming an issue if the enclosure is glass-fronted.
- the 150mm (wide) end was going to be much too narrow for the subjects I tended to photograph. I checked this by looking at zoo photos I'd already been taking (with the 70-200mm), and, using the focal length metadata filter in Lightroom, I could see that I'd taken many more photos in the 70-150mm range, than in the 151mm+ range*
In the end, I decided on the 100-400mm (equivalent on D7100 would be 67-267mm or so). Although you say that you need more reach than your existing 300mm, so perhaps your preferred subject matter may be different to mine. I've been very happy with the 100-400: it copes well for most zoo birds, as well as for far-off ungulates (as, for example, at Whipsnade) and most things in between. It has a great close focus of less than one metre, although I still wish it would go a bit wider than 100mm on occasions. And it's just light enough that I don't have any issues carrying and using it handheld all day long (it has good image stabilisation though, which can help in some situations).
Regarding teleconverters; I do usually carry one (a 1.4x), but hardly ever use it, mainly due to the hassle of attaching and removing it all the time. It's forever off when I need it on, but you can bet as soon as I've attached it then I need it off again!
I usually carry a wider lens too, but that sees little use these days; I was using it for enclosure/exhibit shots, but now tend to use my phone for those, since getting one with a half-decent camera. If you plan on carrying a wider lens to cover your sub-150mm needs, and switching between them in the field, then I suggest trying to switch lenses in a hurry as a tiger, looking directly at you, is suddenly approaching closer than you'd assumed it would - I've tried this and, like most panic-driven lens changes, it's usually a recipe for disaster! A bunch of missed shots, and probably a lens dropped in the dirt!
I guess what I'm saying is, the wide end is often just as important as the tele end for zoo photography. And with a wider lens, you usually get a closer minimum focus thrown in, so it's a win-win. But, as I said before, your preferred subject matter may be totally different to mine, so feel free to ignore everything I've said if it doesn't apply to your situation
* I've repeated this exercise having used the 100-400mm for the past couple of years. I analysed 500 of my best shots: 53% were taken at under 225mm fullframe (equiv to 150mm on your D7100). Only 23% were taken at or beyond 400mm (equiv 267mm on your D7100).
