I've never experienced the Warspite shooting anything without it being tagged first, so that problem might exist even before 3.6.12
The key to the mission is to entirely ignore your primaries (they're a lost cause) and focus entirely on landing good hits with your missiles. This allows you to dump guns energy into engines and/or shields, which you'll need for jinking. You get enough of the missiles to dual fire if you don't miss, but if you tend to miss, shooting them one at a time and keeping track of which side (left or right) it's coming out of is crucial since they don't hit anywhere near the middle of the screen. As long as you're within range of the warspite, everything you hit should be instagibbed, or easily picked off with another tag or a few shots of subachs. If your missile aim is good (try to shoot only within 200m or so, since the missiles are really really slow), and you don't wander out of range of the warspite, the mission is pretty easy. On the rare chance the warspite will instagib you if you're in the way, but it doesn't happen often because your ship is thin. Higher difficulties make it more likely the warspite instagibbs your target IIRC, but of course you don't survive so well soloing waves of shivan fighters on higher difficulties, no matter how bad their guns may be.
I remember your wingman tends to instadie a lot if you don't keep him close, so watch out for that. I keep him close (C38, with occasional C37 micro) and use him as bait while I tag everything.