Cheatgras........UGH! I worked on cheatgrass mitigation all this past summer. Ok, it was all about using herbicides, but still have some experience. So my first suggestion, stop burning. The cheatgrass promotes itself under fire situations. Now that you have it, your going to have it. Some studies show viability in seeds to be up to 30 years (maybe longer) my suggestion would be to start getting rid of seed source. In my personal opinion high utilization by ungulates is the best maneuver. Absolutely graze the crap out of it in early growth. Pending on native composition, natives wont be affected, especially if you have a lot of warm seasons (C4's). Also you need to attack this problem in the fall, if you have high summer/fall moisture you will have another flush come fall. I totally agree with carlson's idea of legumes. Try and plant very aggressive legumes for your area, here in Wyoming it is definitely yellow sweet clover. A tough legume that can stand the grazing impact and help promote natives. If your not doing organics and really want it gone a bit of Plateau could be effective with a lot of other natural mitigation. However the control of Plateau alone is no more than five years. (Sorry had to through the chemicals in there

). But this is definitely a problem that you need to attack head on with no mercy, any less and you will have a serious problem.
And a note on the grazing, it actually does work in Southern Colorado. My families farm down there had a small cheatgrass infestation and start rotational grazing, high utilization, hit the cheatgrass paddocks early, 5 years time, no more cheatgrass.
Thanks
-Tate