First off thank you for your service, second of all, of those, the absolute best would be the EVGA SC17 with a 4K and G-Sync display, however, that is $200 over. It would be the best though, as a 1070 could run the games you mentioned well at 4K and for games where it would struggle slightly, the G-Sync will hide that and keep things smooth. It also has an overclockable processor which means you could turn it up for when you are gaming with a wall outlet around, and ideally gain some FPS. It is really tough, but also heavy.
If you will not always have an outlet, then it might not be a good idea, as it gets 55 minutes full load with full brightness, which would likely mean an hour and a half or so full load with reasonable brightness.
The Gigabyte P57X that I am seeing has a 1080P screen, this helps the battery life a lot. 1:43 full load with high brightness. But it is a 1080p screen... Totally your call.
The P37X has a 4K display, so its battery is likely around that of the SC17 again (sadly I could not find a solid spec for this one)
I feel the 1070 is worth the leap.
One other thing I'll argue though is to consider a 15 inch laptop. they are a lot more portable. I was looking at some for college and these were some that I am interested in:
https
/www.newegg.com/Product/Product.aspx?item=N82E16834233181
This one is the best deal I can find for a 1070 laptop. it has a 1080p screen, but that will mean good battery life, ideally the same as the P57X
https
/www.newegg.com/Product/Product.aspx?Item=N82E16834725033
This one has an overclockable processor and a G-Sync display, but it is 3K resolution. Scaling could be strange in some cases, but this means that the 1070 is almost perfectly matched, and this laptop also has a massive 95Wh battery, which should give it pretty good battery life if you do not overclock 1:40 full brightness max load.
I hope this was of some use.