I recently faced a very similar problem when I organized a King's Indian Attack themed blitz tournament at my club. The problem is that it takes quite a few moves to establish White's KIA position and I had to find moves for black that preserved Black's flexibility in light of the many Youtube videos out there that promise to "crush Black with the KIA" :-).
The solution I came up with was to follow a line recommended by England's "Ginger GM", Simon Williams in his series of videos on the French Defence. It goes like this:
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1. e4 e6 2. d3 d5 3. Nd2 c5 4. Ngf3 Nc6 5. g3 g6 6. Bg2 Bg7 7. O-O Nge7 8. Re1 b6
There are a number of ideas here.
- The King's knight has gone to e7 not f6. This is important because it takes the sting out of e5 by White and of ed. The e file is blocked by the knight on e7 and Black's king sheltered.
- Black has delayed castling. There is no urgency and castling queenside may be more appropriate. In any case don't castle automatically into the programmed KIA king's side attack. Make your opponent think! Try and frustrate his plans.
- Black is ready to meet ed with ed and O-O. If necessary then a5, Ra7 will redeploy the queenside rook along the 7th rank opening up new defensive and attacking possibilities.
- Black will meet e5 with moves like Qc7 and g5 with the idea of exchanging his g pawn for White's e pawn and if White defends with Qe2 Black will happily initiate the exchange of queens on e5. Black is more likely to castle queenside in this variation
- If White follows a traditional move order with moves like c3, Nf1 h5, h4 etc then Black will respond with something like h6, a5, Ra7, Rd7 with threats to play either de to embarrass the White queen or d4 to drive a wedge into the center and take space.
Of course this does not refute the KIA but it does give a flexible and rich way to combat White players who bang out the first 10 or 12 moves like an automaton.