I know you asked MODOK, but cutting on BBB is not a good idea.
Think about the logic of what you're saying. The supergrowth phase is specifically designed for a supercompensatory effect where calories are kept high, and you're going to use it to cut calories lower. I assume your thinking is that the SG phases place less of a strain on the body than the Ramps, which is true but not in the way that it needs to be true (explained in next paragraph).
I don't think there's anything wrong necessarily with using BBB's 2 way split while cutting. But just know that the program is not designed for cutting. If you're cutting, training to near failure that often is just going to be a recipe for injury if you're not very careful about exercise selection. When going near failure that much in a day for high repetition sets, you need calories to support that sort of training. The high frequency is another complicating issue.
If you're going to go forward with cutting on BBB, think more about cutting the volume than about the rest times, imo. For example, taking Ramp1 and SG1 and subtracting either one or two sets from each body part, maybe replacing that with a lower intensity set of the same rep range. And you'd probably do well to go with the 4x split over the 6x. Or maybe just cycle your calories and macros.