If I ever find myself in a position where I have to transport human remains somewhere, I will do it one of two ways:

1- No flying. Drive, bus, Amtrak, or somewhere where there's no TSA and I retain custody.
2- Mail with tracking and insurance. I recently sent a Priority Mail box and a Parcel Post box full of personal items from CA to FL to avoid flying with them [not ashes], and they arrived on time and fully intact.