I have to admit, an all-in attack on Earth seems...unnecessarily risky to me.
Bringing in just the first two destroyer groups, an attack on Mars seems like a much safer bet. Byrne would be very hesitant to commit much force to defend just Mars, allowing Second and Third Fleet to be whittled down significantly in a short time. Then, rotate out the two destroyer groups, and bring the other two in to finish the job with the grand battle at Earth.
With the Hecate destroyers, put their main advantages to bear on suppressing UEF fighter dominance while countering the UEF bomber corps. Trebuchet spam from Herc's, lots of Perseus fighters (also with a bank of Trebs each), flying in close proximity to allied warships.