Since you are quite a bit further north than we are I am not real sure when you would start seeing green up. Cheat will normally start showing signs of life for sure by mid-April here. We try to hit it as soon as it is green, if it hasn't been sprayed in the fall already. Since we are in a 100% no-till system we aren't trying to do anything with the disc. However, I remember well the impossible job that it was to kill cheat by discing.
Would it be possible to not till the area that you are having trouble with cheat in? Just go in and spray it w/ glyphos as soon as it starts greening up, when it is as small as possible and then hit it again with glyphos, if you need it, a few days before you plant your crop. Avoid tilling the area at all if it is possible because every time you run over that with a disc you will be planting more cheat seed. I don't know what your soil conditions are or if it is even possible to try to no-till even a small area, but that is what will probably give you the best chance of cleaning it up.