I think no prayer at a mandatory event is an acceptable solution.
However, since the military really is driven in many ways by traditions and customs, and since these traditions help build cohesion in a unit as they hearken to the history of that particular service, the military would be cutting off its nose to spite its face.
I would advise my commander simply to acknowledge that our different chaplains all have different faith requirements, and that an American who's a grown up would simply have a prayer and recognize differences for what they really are: a reflection of the way America actually looks. This is the grownup response, in my view.
Also, there are some Christian chaplains who are less compelled by their denominations to pray in Jesus' name than other chaplains. Another way to sidestep this is to identify those chaplains and invite only them to pray at these kinds of events.
Also, while allah might be the name of islamics for God, one must recognize that Jesus is one name of God for Christians. (Also, many Christians do not acknowledge that our God is the same God as is Allah. While some might not like that, and they might want to argue over it, it is simply a matter of belief that "allah is not the same as our God."....think of the "Trinity" and their position will become evident.)
(Also, many Christians do not acknowledge that our God is the same God as is Allah."
Actually Allah is Satan.