First off, your campaign sounds quite cool, and is exactly the kind of thing I was hoping to see/hear from the VBAM-Starmada collaboration. 
At first thought... weapons that ignore shields would remove part of your problem and then reduce the issue only to PDS. But as you have already pointed out you are out of time to research and prototype a new weapon system.
I know with the xenophobic any attempt to force diplomacy on them is probably tough, but I would screaming for a ceasefire and a treaty, no matter how much it favored the aliens.
But, looking at what you have...
Extra-hull damage is sweet, if you can get it by the shields. Match it up with the Increased PEN and just throw volumes of fire at them to try and overwhelm the defenses. With what you have, I would think cheap gunships - seriously over gunned frigates or destroyers - armed with Xhull and +PEN at long range and squeeze a Stealth Generator into the hull if you can. Go cheap with AB arcs... no time to be fancy or hope the ships live long. Hopefully you already have design that fit the parameters. If not... probably running into prototype issues again.
You could do the above but strip the hyperdrive... start piling them up to defend Earth.
Marines? Do the enemy use many security forces? If they are vulnerable to fighters, you should be able board them and just overwhelm the crews to take the big ships out of action.
And get ready to rip those buoys... the human race may depend on it. :cry:
(The only thing you are "missing" on your shield mention is the cost... A ship so defended would lack much in the way of weaponry, unless they had tech to balance it out. There is a chart out there somewhere on the utility of PDS vs. shields at certain levels /sizes. I forget the details of how it pans out...)
