I live in NZ.
Note MPR's advice and carefully consider whether this trip is liable to be "the exception that proves the rule" -there are enough scenes in NZ where the photos of a lifetime cry out for the long lens.
As Olin says - NZ is relatively small, but what this means in reality is that frequently have a vast range of 'photo opportunities' presented to you.
At full zoom of your ...70mm amd ...300mm lenses the area difference covered is (300/70)^2 = over 18:1 (or about 13:1 at 250/70 if you avoid the very extreme lower quality end of the Tamron). There will almost certainly be times when being able to photograph say 10% of the area covered by your 17-70.
Unless you are going to pass up all photo opportunities outside your normal range, in your position I'd add the Tamron to what you propose. The difference in weight is not vast. NZ is generally secure enough that a lens left in a car boot when hiking is much more likely than not to survive the journey. Car breakins do happen, but in 40+ years of driving in NZ neither I or my family have experienced a car break-in while travelling. (I've had several car windows broken when the car was parked on my property).
Why you need the long lens :-)
The image below is too dark at the size seen below to make the point well.
The larger version viewable by direct on imgur access does it better
This is a 6 megapixel photo taken 7 years ago with A Minolta 7D DSLR. I chose it because it was taken at 200mm. It's a view across Auckland harbour from near my home. The right hand image is the same image scaled down by a factor of 70mm/200mm = 35% linearly or 12.25% (= 0.35^2) of the area. Foot zoom does not work here - unless you swim really well and have a waterproof camera - and then you miss the shoreline reflections and the angle changes and ... . ie no matter what the ground in between was like, the image would change if you moved position. If you were by a roadside and there was a glorious NZ landscape afar off, you will often not be able to get closer. There is so much that you might be able to do with a long lens that now you have read this, if you leave it at home, you will regret doing so forever :-).
70 mm / 210 mm comparison:
I took this photo this afternoon specifically to address this question. Taken "at a venture" from a car at 100 kph. No claims made as to photographic merit OR the crops, whose size is set by the example requirements. I use 210mm as it is less than the full available 250mm, as quality usually drops at full zoom. Also as 210/70 = 3:1 it makes compsido
This is a view across Auckland harbour to the city from a car on a motorway. You can't stop, you can't move closer and even the framing is decided mainly by the situation. If the 70mm and 210mm shots were full APSC frame then the content in the 210mm image would be vastly superior.
The top left photo is the whole frame at 200mm on an APSC DSLR (Sony A77).
The 3 crops A B C are 1/3 the width and 1/3 the height of the original so would be the whole frame if the scene had been photographed at 210 mm. The 3 crops were aligned to approximately surround differing and significant parts of the scene. If actually cropping or framing to suit content material enclosed would probably vary somewhat and the right hand crop may have been extended out of the frame to the right to include the whole fleet of boats. Rectangles shown are fitted by eye to match the crops and may be a few pixels out.
Larger version here - click this link then click resultant image to enlarge