Why would KJ sign the ball #11
Ah-ha! This is an important detail I didn't pick up on earlier that leads me to revise and narrow my guess as to when the ball was signed.
I now think it was at the end of the 87-88 season. KJ was traded from Cleveland, along with West, on 2-25-88 and wore #11 the last two months of the season before switching to #7 for the 88-89 season (he wore #11 in Cleveland).
Gattison is listed as playing for the Suns during the 86-87, and 88-89 seasons, but not at all in the 87-88 seasojn, so this leads me to believe he was injured, but still with the team. Hornacek was still there also.
Therefore, the ball had to have been signed between Feb 25th of 1988 and the end of that season. If the signatures were all collected at the same time, including Richmond's, then the ball was likely signed at one of the Warriors' visits to Phoenix on either March 30th or April 19th.