The crop to DX feature of the D800 family to me is a excellent tool. I find that I use often and would rather crop the shot in camera, than take a huge 20mp shot and crop it later in post as I did with Canon. As to 7100 vs D800 to me it breaks to down to the sensors. The 7100 is noisy much past 1600 and is always cropped. The D800 can shoot clean up to around 3200 and if you push 6400. The other plus to me is having the amazing range of DR at iso 100 which the 7100 will not have. The DX mode to me is the better solution since I can still use all FX lenses and not have to carry a DX set to get the best from the 7100 or similar camera. When I need the crop, it's there and using by far the best part of any lens, i.e. the center.
The 7100 (as all crop sensor cameras in my experience) will also have issues with wides, especially if you use a DX lens as it gets pretty hard to resolve to the edges of the 24mp sensor, thus requiring a crop, thus bringing the final resolution more to like 18mp.
My thoughts were pretty much the same as yours on the use of a crop sensor and I hoped to see better results with the 7100, however it pretty much mirrored the Nex-7 I have (believe the sensors are pretty much the same also). The Nikon 7100 does do better on noise up to around 1600 or so, whereas the Nex-7 is pretty worthless past 800.
To me the sensor in the D800 or 800e is pretty much the best thing to come along in quite a few years and so far has yet to be surpassed. Having a 15mp file in DX mode is a huge advantage especially if you are shooting wildlife. Not to mention the savings you get on the card not having to shoot a full 36mp file each time.
About the only downside I can see to the D800 is the size/weight of the body with grip (I use the grip) vs the 7100.
Enjoy the trip as it's a beautiful place.
Paul Caldwell