Nothing prevents from making the "Time" dimension yourself as a regular dimension, basicly it is a simple hierarchy. Of course then you loose all nice things like Relative time dimension, but if you wouldn't need those. I guess, then you could have your LastDofM/not-LastDofM as an alternative drill-down.
But one thing which will prevent this approach is if your measures need Time state rollup: Last period (or similar). Or you would at least have a big workaround to invent.
Cheers