I really doubt the exodus is going to happen. Would the elders be able to move the 18+ billion men, women and children of the UEF to an alternate universe? How would you feed them when you get there? This isn't a war about which ships blow up which; the UEF is trying to protect its home and its people.
The project obviously involves the Bei's, because Sam mentions working on something big to his father. Then there's Laporte's abduction by the Fedayeen and that particular elder's (I forget her name) discussion during the mission with the Pegasus ambush, which shows the Council's interest in psychics. This is an extension of project Nagari (that's the name, right?). Basically ETAK 2.0
The stuff above is hinted heavily enough in the campaign that it HAS to be something involving contact with the big otherworldlies. I think the real question has to be: what does the UEF want them to do? What will they do?
The Vishnans are non-intervensionist, for the most part. They stay out of almost everything (FS 1+ 2) or they're really, really, really subtle. Their deal is to make sure the natural order of the Universe doesn't fall apart. The UEF's been listening for a year, but the Vishnans have said nothing. They don't have any qualms about talking to squishies when its important (AoA), so either they want to leave humanity to solve their own problem or the Shivans have them all tied up. The absolute most I can see the Vishnans doing during the course of WiH1 is just making sure the Shivans don't follow their nature and swoop down on all the chaos and bloodshed with beams of red death. So I don't think Byrne's calling the Vishnans.
I think he wants the Shivans.
First, in a totally meta sense, it doesn't seem to me like the BP team would resort to such Deus Ex Machina as to have the great lawful-good force of the universe come in and save the heroes at the last second. These guys love to work with moral ambiguities. That the good guys would get so desperate as to make a deal with the devil offers some complex story potential.
Second, Laporte's visions differ greatly from Sam's. The Vishnans contacted him (relatively) peacefully and tried not to totally shatter his mind. Ken showed up to Laporte in a red nebula, telling her that she must "destroy in order to preserve." We know that Shivans are at the absolute least familiar with nebula's (FS2) and I'd go as far to say that its among their "homes," as opposed to the weird spectral landscape of the Vishnans. Plus FS1 tells us that the whole preservation/destruction connection is probably a Shivan ideal.
Third, we don't know a lot about Byrne other than that he's cautious and careful with his own forces. The impression I got, (though this is up to interpretation) is he's a good man being pushed to his emotional extremes by the hand he's dealt. He knows he's running out of time. With things getting so close to the wire, would anyone be so surprised if he lost sight of his ethics, even for just a moment? The Vishnans aren't coming, and his super-project needs steam. Luckily, the preservers aren't the only kids on the block.
So we've got the Fedayeen picking up a psychic super-conduit to the Shivans for Byrne's secret project. I'm almost certain he means to contact the destroyers. But what then? My guess would be to launch a third incursion in GTVA space. If it were big enough, Steele would be forced to relinquish a large portion of his forces. Byrne might be hoping to force the GTVA to partner with the UEF against their common enemy, and in so doing forge an alliance similar to that which ended the T-V war. Although, I have a feeling this would go horribly, horribly wrong.
