Rabbit, Sorry for the loss of your father, and for the loss of lifelong treasures. Nothing will make up for their loss, and sadly you will just be a claim number to UPS.
When I was in the funeral home we always used USPS. We started with it, because they are the only ones who will ship cremated remains. We would use the same tracking level (Registered) for other family valuables. We never lost anything, and if something would drop off the tracking radar, one phone call, and it would be found quickly.