...Then he gets on 305 and because he likes to act like he knows everything, he does not need to look at the cards...?
Somebody looked at the cards - at least one, the packing card with the serial number SN 60-9797 written on it. But, somehow during the skyjacking that packing card was transferred from the chute on Cooper's back to someplace on 305, maybe on, in, or near the not-used back chute. Then in Reno, a skydiving expert from the National Guard found it and decided - rightly or not - that it was for the "not-used" chute. Then that card was placed somewhere else, possibly put in an FBI evidence envelope, and eventually made it way somewhere - possibly the FBI FO in Las Vegas - and it may still be there today.
Then in 2011, the packing card known as SN 226 was discovered and photograph in Hayden's "not-used" chute. But packing card SN 60-9797 was not found on that chute.
That's what we know about the packing cards, as far as I know at this point.
My conclusion, and possibly that of Fly Jack as well, is that there were two packing cards for back chutes on 305: SN 226 and SN 60-9797. That means both chutes were Pioneers, both were Hayden's, and Cossey is lying about it all.