Disagree. You did it right. The rule is specific that if the ball falls from the tee "...for any reason..." that the play is to be stopped, i.e., "do over." There is no limit to the number of times this can happen. There is no actual rule compelling Team A to have a player hold the ball, but it has been accepted practice to allow Team A two attempts without a holder, then 'encourage' them have someone hold the ball on the third attempt. But, even then, if the ball falls from the tee, we have our 'by rule' marching orders. I'd counsel the holder to not let go of the ball, but, they still get the 'do over,' with a fresh play clock.
Related side story. A particular crew always had a crew member prepare a 7 question quiz that they would review during pre-game at the stadium. Working at Nebraska one day, one of the questions was this very 'ball falls from the tee' scenario. This crew hadn't ever had that happen, and, up to that point had not discussed it - from a rules or mechanics perspective. Crew discussed who should see this and how to handle it. Middle of the first period, Nebraska kicker is advancing to kick the ball, and a half step before he kicks it, the ball begins to rock forward off the tee. All four 'up' guys immediately sat down on their whistles and moved into the field with big time-out signals just as the ball was getting kicked. They properly shut it down and 'reloaded' and ran the kickoff again. At halftime, they all looked at each other and agreed that it was truly spooky that this scenario had come up, only a couple of hours after they had discussed it. But it was awesome, because, as a result, they were "all over it," as we sometimes say. Ah, the value of preparation...
