I hesitated to comment on this one but thought I might help out. I do admit that after a lot of years, some things are a little more forgettable and others are very clear.
First, I would guess that there was actually more than one game ball from that game. As far as if Jack had one, he probably did but by the time the movie came out, Jack was retired and wasn't working out of an office.
Second, I do think McMullen (or Mac Mullen as Red always called him) was in place fairly soon because he asked Ohio's AD for permission to talk to me during that basketball season and he also introduced Dick Bestwick as the new head coach at a home basketball game. So Jack definitely came after Joe.
Third, I like and liked Red, given what he had been through it was extremely tough for him to be told he couldn't have the HC job but he could stick around and be an assistant. I am so happy for him he's achieved some peace. He more than deserved it.
Fourth, I agree with him about that Miami game. Miami did play their 3rd and 4th string a lot.
Fifth, I'd like to say some things about Joe McMullen but he's gone and can't defend himself, so the best thing is just to say very little at all about him. I did end up at Marshall because of Jack and not because of the AD. A lot of people from back then have a lot of Joe Mac stories.
I have not read the book but I am sure I will get a chance this year. Red deserved to be as bitter as wanted to be back then. No one should have to go through what he went through. The same for all of the families, the fans, the students and the entire community. It changed the history of Marshall University, and while the years will eventually take a toll, and no one alive will remember being there then, they will be able to see and know that the fight to go on was there then. And remains. So salute Red, Jack, even old Joe Mac for having the fight in them. From first hand experience, it wasn't easy.
Last thought: If anyone should have been part of the movie and your memories, I cherished my time with Ed Starling. He was first class. I think it would have been easy for him to go away and move on to something else, but he stuck it out and was a very steadying influence. He's one of the good guys you are fortunate to meet along the way.