About a month or so I started using fins for the first time, and feel like I have really improved my 2bk that way. As you say, kicking gently with long fins really amplifies the feeling of how the hips are acting.
To start incorporating that feeling even more, try doing some lengths with only one fin. Then you can start to match the feel with your other leg too.
These days I am doing this set during my tune-up most days:
2 x 25m with 2 fins, gentle kicking only for 10m, then add arm strokes
2 x 25m with left fin only, full stroke, trying to match right leg to what left leg (with fin) is doing
2 x 25m with right fin only as above
2 x 25m 2 fins, full stroke
2 x 25m no fins, trying to maintain same feeling in kick
This helps me a lot to keep hips engaged and kick working well. I believe I picked up the idea from Zenturtle here on the forum.