Welcome to the club! I don’t have any specific solution to your problem. But I can share with you some useful points.
First, imo, not withstanding stats, it is a general defense problem and not a opening problem. Both sides have short castled and one side has better space on the king side. Colours reversed, white can have similar problems in, lets say, 4.e3 Queens Indian. Black in that case can play Ne4, f5, g5-g4, Qg4, Rf6 etc. Similarly in your case f4-f5,g3-g4-g5-g6, Qd2-g5 etc. It can be quite menacing and one mistake can cost the game. I’ve been there.
In this case, shifting the knight to e4 if possible and playing c8 bishop to the long diagonal, strengthening the second rank defense with Rac8-c7, Qe7 etc and not moving the f,g,h pawns till the last moment are the standard defense techniques.
Seeking active counter play on the other side of the board may be difficult. But what is needed is passive defense on the king side while simultaneously preparing for future play on the queenside. Silver lining is that white has to make lot of concessions on the king side for such type of double-edged play.
Of course, none of what I wrote may be new to any of us here. The point I wanted to make is, a good book on defense is likely to help you better than ECO and DB stats. You might want to study the limited number of Black wins and draws, in this perspective.
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