I may have figured it out. There is an option to add leaders to the den, and one of the option is Tiger Adult Partner. There is also a Lion Adult Partner. Once I set one of the parents with that leadership role, I was able to invite them to the event as a second active leader, and it let me save my event. I will give all the parents that role, and I think the problem will be solved, at least for me. I could not connect the Cubmaster, but I may not have the needed permissions as Den leader and Den Admin.
I don’t know how this will work for ranks other that Lion and Tiger. I don’t see an option for Adult Partner for other ranks, so I guess someone would have to be designated Assistant Den Leader.