Hammers generally have great reviews as far as terminal performance, I haven't seen many negative reviews of them. I have seen lots of bad about Bergers, though personally we have taken over 80 pronghorn (mostly), mule deer and elk with them and never had a failure. It may be that most of our game in that number is very light pronghorn does, or that the closest mule deer/elk we have taken with them was still over 400 yards and mostly 500+, or that we always use a wire drill to clean the tips out, or we always use the proper twist rate and then some, or maybe we have just been lucky, I don't know, but they have worked for us so far.
We killed probably around 20 critters with the .277 170 specifically, from 300 yard pronghorn to a 940 yard elk, (also had a 70 yard pronghorn, but that was a neck/head shot, so doesn't really count for terminal performance) and it performed the same as our other Bergers. On the elk, we weren't consistently getting exits, but we never seemed to need them, they died within sight of where they were hit.
However we switched to the 140 SBDII because it gave as good/better ballistics than the 170, and we were hoping to always see exits and hopefully as good or better terminal performance on game. So far, that is what we have seen. It is a very small test pool though.
Personally, of your choices, I would just cut out the 126, it won't be sufficient at 1000 due to low velocity and energy, not to mention a ton of wind drift. The 170 and 156 do make minimums, and the 156 isn't a huge amount of wind behind the 170, about .75 MOA, if the Hammer listed bc's hold up in your rifle. Either would be sufficient.