...Well, blast, I guess my counter-offensive won't work. 
My revised recommendations:
In the north, I think it's worth it to move some fleets around and take some casualties if it means eliminating or crippling the 1st Zy. They are still very strong, and again, this game's battle system rewards making the first attack. If we just try and stall them, they'll keep mangling our fleets on the attack, give the Hierarchy another attack route in the north, and threaten an eventual breakthrough. Just kill them NOW, take back Tauri, and then we can use those fleets to hold Aldebaran easier / fend off any more flank attacks in the area.
The situation in Aldebaran is stable for now, especially with the 2nd UGCR in the area. I still think the 1st LSF and its 4th Gen fighters would be put to better use in the south. At most, I'd say bring the 3rd DD up north.
In the south, we have to respond carefully or risk getting overrun, especially if we can't attack Kardoen and the fleets there will be attacking Hydra/Draco next turn. Nothing personal, but I think we desperately need the 1st LSF to reinforce the fleets currently defending Draco. Hydra should hold if I bring in the 4th CRF, but our fleets in both systems WILL be getting savaged, and we need reinforcements on standby to relieve both our fleets in Hydra and Draco. If we don't have at least 4 fleets covering both the Draco-Vega and Hydra-Odin axes, I fear the Hierarchy could shatter our defenses and break through by committing enough forces.
Even if we can't do it right away, I think we desperately need to eventually counter-attack into Kardoen and seal off the flow of Hierarchy fleets into the south. As long as we have to defend two or more systems at once in the south and the Hierarchy can keep sending in more fleets through Kardoen, we'll eventually lose the battle of attrition. To push them back, or even to hold in the south with more enemy fleets undoubtedly inbound via Kardoen, we'll need to commit as many fleets as we can while leaving enough to keep the north stable. With some adroit maneuvering, we can still defend the north without sending heavy reinforcements there. The south is a different story. I know I sound like a broken record at this point, but seriously, we could lose the war if the Hierarchy breaks through our lines on either the Hydra or the Draco axis.
Simply put, I don’t think we’re going to take back Tauri. They’ll just move another fleet in there. Then another. Then another.
And we can’t kill the 1st Zy right away, it’s too strong. I think you underestimate how precarious things are up in the North. You’ll still get your 8 fleets down South with my plan.
I want to wear the 1st Zy down,
then finish them. We can keep them under control and weaken their strength. If they stay in Tauri, the next move would be to have the 4th SF resupply again, then go to Tauri to take the next hit at full strength, as the 1st SF pulls back to resupply.
Anything could come through on the next turn up North, another Zy fleet perhaps, or we might even get the Hertak.
Hertak or not, once the 2nd Nordera is wiped out, you’ve only got 4 fleets down there, it’ll be 2 on 1, and the Nordera fleets are pathetic. It’s best to send the 1st LSF up here. If anything, their power will help us to finish off the 1st Zy when the time is right.
Remember, even if we manage to fill up Kardoen with our fleets, they’ll still be able to move past and attack Hydra, it’ll be the same as up North with Tauri, I don’t think we’ll get it down to one entry point.
So, I think it’s more important to focus on ways to eliminate enemy fleets rather than taking Kardoen, because, I just don’t think we’ll ever take it, the enemy are only going to get stronger, we need to destroy fleets, we need to keep a numbers advantage so we can pull back fleets, resupply, and rotate in and out.