IMHO one root of the issue is that bigger ships don't sacrifice speed or agility. In some aspects (like the ability to permaboost, or turn rate outside of the blue zone), they often *gain* it over their smaller counterparts.
This is compounded by engineering.
I think it's far too late in the game to contemplate the ground-up rebalance you'd need to fix this. But if it weren't, and I were in charge, here's where I'd start experimenting:
* Medium ships would have reduced turn rates. Large ships would have *greatly* reduced turn rates.
* The bigger the ship, the more critical it is to use the blue zone (Not less, like it tends to be now. pre-engineering FAS and Anaconda turned faster outside blue than an Eagle and it's only gotten worse).
* The bigger the ship, the less extra agility it gets from boosting. (On the other hand: larger ships would have *longer* boosts to use instead).
* Likewise, the bigger the ship, the less you can perma-boost.
* Chop top speeds down to roughly the scale they were at pre-engineering.
* For that matter, engineering becomes a lot more side-gradey, with more costly tradeoffs.
* Turrets would be a lot more effective. Rather than being too low-damage to be useful, they'd do the same damage as gimbals but take too much power to be practical on smaller ships.
Lucky for you I'm not in charge, since basically all of these would be wildly unpopular.

And they may not even work, but if I got to design a flight rebalance beta, that's the sort of thing I'd be looking at.