I usually do that RP, but in the case of the stingray the hooks were so far down it would have been easier to locate them from the other end (so to speak), but I have no desire to become a proctologist.

The eagle ray was hooked in the mouth (both hooks) this made it easy to release and yes it was flipped upside down.

It occurs to me whilst for personal safety it is wise to upend them, I wonder if this disorientates them for release? This makes sense as no fish naturally swims upside down.