I tried the Cinch knot again and had better luck.  The Perfect Loop is an oval sticking out to one side.  I also tried to pull the knot down too tight.  One thing that helped was to start off  by wrapping the wire around the nose of needle nose pliers until it retained a 135° bend about 2 inches from the end of the wire.  Then put the swivel on the wire and tie the knot.