When dealing with large egos, it is absolutely necessary to be seen as in charge. From personal experience and being one who can have a large ego, I will walk all over or try to manipulate the person in charge if I see they are being weak or indecisive. It?s not something that is intentional, it is instinct. Like being an experienced and talented hunter. You just know what prey to take that will be the easiest.
A team of developers with a minimum of eight years of development experience cannot have entirely different ways to reach the specified goal. However, if their egos are as large as you imply, then they may see their ideas as completely independent. Perhaps it would be a good idea to review the various proposals and ideas andfind some commonality among them. Sure the ideas may be presented in different terms with different words, but a rose by any other name is still a rose. Then from there, find where they diverge.
Then sit with them, go over the similarities. A person with a big ego will then latch onto how different their ideas are then the others. After all, they are vying for rank like rams during mating season. Once everything is established and positions are taken, consider doing what the Senior VP of my company did during a battle of developers who wanted their projects put at the top of the list.
He got the developers and asked them who would stake their jobs and reputations that their ideas would work and are the best. No one stood up, and they went back and began to review the other proposals.
Big egos wont put themselves in a position to be publicly humiliated in front of executive management