What should I be doing while burning all of my resources to get G11?

If this is your main echelon, ditch STEN and try to level up a third AR while you wait for G11 to come home, preferably M4A1. Just keep leveling your main echelon, try to start a couple of secondary echelons using any other good units you've gotten along the way (the story ARs and RO635 are all quite good choices), and make your way slowly through the story missions. You'll eventually craft who you want, but the main thing to focus on for now is getting at least a couple of echelons to x4 or x5 links.

You probably want to want to make an echelon with 3 ARs in the backline (M4A1 and AR-15 are very good options) and 2 SMGs in the midline, so it wont lack damage.
About what you want to do: Try to clear the campaign -RO635 is an awesome tank- and get to at least N2-4 to unlock the equipment enhacement/calibration. In order to clear night battles you might need 1 or 2 HG/RF echelons or ARs with enough damage to punch through armor (9A-91 and Mk23 are good options).
Another thing that you might want to try is S-ranking all the maps to farm the gems. You'll need at least 3 usable echelons for chapter 5+
Dont keep waiting for the rolls, that will come by itself as you play! GL HF