I've been thinking about going down South, but it's a bad time, due to what will happen to the 1st and 2nd UGCR fleets when the mercs wear off and they drop down to like 40-60% health. Here's a situation I'd be comfortable going down South:
This turn, we wipe out the 5th Cordi as I laid out earlier.
Next turn we have the 1st UGCR pull back and Resupply, while the 2nd UGCR continues to recover and everyone else attacks the 3rd Cordi.
The turn after, if there still are no new enemies, the fleets in Crux can take Crux, while the UGCR fleets get merced back up and enter Algol. Then we can send two fully merced up fleets down South.
If we wiped everything out up top, then everyone could then come down. If more enemies arrived, our respawned fleets would by then be in a position to move to intercept.
I'll be very surprised if we don't see more enemies though, especially a 4th Zy Fleet.