After reading the entire thread (whew that was long)...
The GTVA simply doesn't have the resources to defeat 80+ Sathanas. Even taking on one every 15 minutes, the losses would be immense. Ok here's a blockade scenario for you... you scatter at least three wings of heavy bombers and at least ten wings of fighters. Around a node, everyone scatters so they don't bounce off a Sathanas. So, the Sathanas jumps in and is ambushed--the fighters immediately go for the fighter bay--as you can't fight if you can't escape. the bombers take out the engines as well. After a few minutes, the bombers can basically run out of weapons range and wait for the next Sathanas. If the next one jumps in, it will collide with the first Sathanas--and be in good range of any following Sathanas. When Sath #1 is parked and Sath #2 hits, destroying the front arms. The impact puts it closer to the node--where the bombers can quickly disable the ship. Now you have a problem--you'll have swarms of Shivans attack shortly, though the Sathanas problem is taken care of. So you'll probably be expecting at least one more Sathanas to jump though, right? Wait for it... waiiiit for ittt... *bam* you've solved at least one problem by now--it's most likely that the middle Sath is out for the count and the other two are heavily damaged.
Next, you need something to stop the fighters. We can't simply build a Dyson Sphere around it, so we have to do something else. My personal way to stop this would be to launch Ursa bombers, filled with Rockeyes. Have them constantly circle the node and have the turrets aimed towards the incoming fighters. This would be highly effective in the short-term... not much of a problem. We can assume that the Shivan fighters can't jump from one system to another (why? because... they've never done that before... and after the Ravana was destroyed, we had no more Shivan fighter problems). So we still have a large problem--the Sathanas are all jumping in with fighter-bays intact. We have to solve that, ne? Easier said then done. Our best system would be to disable the rear beams and bring cruisers in to destroy the bay.
Now it's a waiting game--the Sathani are disabled and heavily damaged, and they can't get much more support. The shivans can, however, send in destroyers and other smaller ships. So they do. In comes a few destroyers. Same procedure, right? Right! Only this time, make sure we disable them, take out their fighterbay, and destroy all beams. So now you have probably 2 sitting-duck destroyers as well as 2 sitting-duck juggernaughts clogging up the node. What to do for the Shivans? Suicide, in short.
I hope that demonstrates a way we could actually STOP a Shivan advance. With enough time (probably 1 hour for this battle), we could clog the node. They'd probably send a few Sathanas to destroy the others to clear a path. Rinse and repeat--every time they send in a sath, disable it and wait for another Sath to destroy it. Eventually they'll pull back or we'll kill enough of them that they simply leave.