Mileage must be actual and must be recorded from one point to another. If I am reading you right, you are picking up assignments between other unrelated jobs, as I used to do. Record your OD readings as you leave for the MS assignment(s) (regardless of where you are) and until you reach your non MS destination(s)...........that could be your home or your other job. Your tax consultant may have a handy "car friendly" tool for this. You can add up the miles from there.
My tax consultant has never asked for odometer readings, just total miles for my MS work and total miles for the other job.