I've never worked in a situation where the per-diem was an all-up number intended to include airport transportation. That seems illogical, given that the first and last days of a trip have the unusual expense of getting to/from your home airport, plus the transportation in the work city. It's no longer a normal daily expense in the spirit of per diem.

In any case, when I did work for a client who reimbursed individual meals on a flat per-diem rate, we used dayparts. Arriving home Friday morning would be a 25% or 50% per diem. But that was essentially just covering breakfast, as we expensed taxis, parking, mileage, etc. individually.