I agree with the OP that missiles have a pretty wild swing in power, with the trend going downward fast. I do think that rather than go through a major rewrite of code, that one of the previous mentioned solutions would be a good place to start.
Modern fire control systems have an upper end on the number of targets tracked, and missiles that they can reliably control. I think that would be an easier path to chase rather than dropping agility and changing accuracy across the board.
Cheesing missiles by sandpapering a target with Size 1 ASM's have been around since the VB6 version. The reason its so effective is because its cheap, and you can lob massive salvos that can swamp PD, no matter how sophisticated.
If you look at the history of air to air, or naval missiles, the original fire control systems were one for one. In other words, a single radar fire control would 'lock up' a single target and then guide the missile in. These early missiles were "beam riding", or they follow the firing plane or ships radar to the target. This worked, and is still used for certain applications, but suffered from attenuation over distances. These early systems had limited numbers of missiles they could control, and were not especially effective (example; the early Sparrow series of missiles).
The ability to track multiple targets, and engage them only started to really develop in the 60's in a limited format, and then really develop in the 1970s with the advent of microprocessors. During this period, missiles were dependent on the launching platform to maintain a radar lock to guide the missile in. Later missiles changed to Semi-Active Radar homing, which meant that the launching platform still 'locked up' the target, but the missile could follow the radar reflections to target itself. This made it easier to launch and control multiple missiles.
This was also one of the driving factors in "fire and forget" weapons, that could take target information and track the target themselves.
How this translates to Aurora:
Limit the number of missiles controlled per Fire Control. So for example, if the control limit is 12 per FC, then a ship could launch three salvos of 4 and could control them, or a single salvo of 12 and control them all the way to target.
UNLESS;
The missiles have their own sensors. So, for the example above of 12, in which case the firing ship can program and launch up to 12 missiles per salvo continuously.
In that way, missile cheesing is throttled by the FC limit, and since size 1 missiles wont mount active sensors, the box launcher sky barfing method is nerfed. No other changes needed.
It also incentives the use of active sensors on missiles, for those who want maximum rate of fire and salvo sizes, which in return is going to mean bigger missiles to mount those sensors. Missile agility is still a viable trade off.
This also reflects the way missiles are used today. Anti-missile missiles, like the SIM-2, still use beam riding technology, since they are made to be cheap, fast, and short ranged defensive missiles. Larger anti-shipping missiles are either pre-programmed and fired and seek their own target (like the Tomahawk) or they are semi-active and guided in until they are within range of their own internal radar.