Is there a good way to store the string so it doesn't lose its twist & I don't have to pack a bow square?

I always just put a twist tie through my string loops when they're off the bow. That keeps them from untwisting.

Take an arrow and hold it with the nock against the riser and make a mark with a magic marker on the arrow where the string is to mark the brace height you want. Now you have a tool to measure brace height and you don't need a bow square.

Trust me, the magic marker mark will not change the "tune" on your arrow. (Before someone asks). 

R

We have done as Ryan suggested but usually throw a bow square in our luggage.  But, simply threading one loop through the other and then pulling down on the end with the loop that you threaded through works.

For trips into the African bush, we also take extra strings that are ready to shoot as well as serving/tying string, nocks, nocking pliers, and even a fletching jig with some fletching.  Im sure that Im forgetting something.

 We manage to keep our duffles under fifty pounds with all of our clothes and gear.   We've never needed to launder any thing while there for a just over a week and that's changing hunting attire daily.