There is no currently available way to force the REx on earlier in the NA market (at least in the USA and Canada...not even sure if they are selling it elsewhere in NA yet).
The car will go into battery preservation mode at (if I remember correctly) 1.9% on the REx, and the REx won't come on until it's around 6.5%, so if you are stressing things (i.e., using more power than the REx can provide), you will continue to draw down the battery reserve and eventually hit that brick wall.
The only way around this is to either find a charging station to top off, forego some of the creature comforts - switch to Eco Pro or Eco Pro+ mode earlier on in the trip, and maybe take advantage of all of the prompts to help you go more economically, or, take a different vehicle or route.
I'm been saying this on this forum for awhile...it really depends on where and how you drive whether the car, BEV or REx will work out for you. It is designed as a city, commuter car, and at that, it does well.
2011 535i x-drive GT, 2014 i3 BEV