Last time I checked, the Second Shivan Incursion didn't begin with 80 juggernaughts, but with a mere couple of rakshasa and a few wings of fighters. For a good while the GTVA didn't fight anything larger than the first Ravana. The GTVA probably bets on that delay to be able to either hold the line or evacuate the systems until reinforcements arrive. 2-3 corvettes per system is probably enough, with a destroyer at, at most, one inter-system jump away.
Laporte mentions in Post Meridian that the Tevs have two dozen Hecates. That's enough to put a destroyer in every known GTVA system save three, even without the help of the Orion/Titan/Raynor classes or the entire Vasudan armada.
As for the GTVA's strategy, I think Steele has a better grasp on the situation that even we do. If the Imperiuse has been tucked away in the Kuiper Belt since Darkest Hour--and it's reasonable to assume it has been, since you're up against its fighter wings in the very next mission--then I have to wonder why he kept it hidden, rather than shock-jumping the Eris or Toutatis during one of their sorties to buy time for the Wargods. The only thing I can come up with is that Steele is fully aware of Byrne's
secret project, and that he wanted the Imperiuse to be a secret trump card, and only exposed it because he had no other option to save the Carthage.
I would say push while the UEF is still reeling. The sooner 2nd Fleet Mars and 3rd Fleet Jupiter are broken, the sooner the GTVA can actually focus on Earth. Assuming, of course, it doesn't push Laporte over the edge...