Hah. That's nice.
Maybe not quite a relevant question for here, but were these ever implemented into a release, or just put up on the wiki? I downloaded my install not that long ago and my Purusha/Karuna entry doesn't mention anything about it.
It seems to be a very recent BP Wiki update.
The thing is that GTVA has at least four Erebuses and perhaps thirty other destroyers to throw at such a problem 
Tevs cannot mobilise such a great force against the UEF, as the UEF aren't the Shivans. I'd say that they cannot push more than a couple destroyers into Sol, there were about two mentioned that were already underway to be sortied. GTVA can't leave its systems unprotected in case Shivans come back - and there's a lot of mystical Nagari stuff going on lately which could make them respond to it. In their typical way. Heck, even Shambala might get their attention, and probably GTVI knows of this. Plus, the Sol gate has a pretty low capability of transferring vessels, the limitations of new technology and lack of energy to imitate a "normal" jump node. If the UEF takes control of the Sol side of the node, they could just wreck anything that passes through, and the gate's limitations would make the flow of enemy units really slow. And political reasons - if Carthage would die in Delenda Est, political disapproval could force Tevs to halt their war machine. A similar thing, but on a bit bigger scale might do the same at the "current" BP timeline moment.
ELDER: "The project is called Shambhala. It began twenty years ago, but the final breakthroughs were not made until the 14th Battlegroup defectors brought their expertise to bear."
It's not like UEF didn't know of Nagari before Capella. They seemed to research it even before Sol was stranded in space (GTI had some interesting discoveries like the Idun Dictionary), which could mean they were a bit into Nagari already. They could have got some subspace readings of Capella, detect Shivan Nagari activity from there, or get a "hint" from either Vishnu or Ken (it seems he's got some wide influence - Laporte, some "others", presumably like her, and probably also the Hammer of Light, remember what did one of them give to Laporte?).
What did 14th bring to the project? Well... Possibly meson, beam or/and subspace technology, but also a load of Nagari-sensitives and data from the entire AoA. And one more thing - some say, that it is a war machine, others that it involves a lot of mystic stuff... Since the UEF is already barely standing, I have a suggestion: why not both?