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Fortress-like Position: Is it a draw?

I recently played an over the board game at a local tournament against a 2000 rated player with the black pieces and I ended up getting this position.



www.chessdrop.com/jXm6u2b4W7mmWXNMc

I eventually lost this position when after 30 moves he found a winning plan of getting his king to g5 by invading e5-f4-g5, and trading his f2 pawn for my g6 pawn and winning the resultant end-game. I parked my knight and g4 and wouldn't move it and ended up blundering the position by moving it to h2 then his king was able to invade that way. My question is if I put my knight on g4 so e5 is blocked, and just shuffle my king back and forth is there actually no way to invade? The computer will tell you it's +2 but I know they really tend to misevaluate closed fortress positions if they aren't that strong. I had the computer play against me once i knew to place my knight on g4 and it couldn't find a winning plan. Can anyone with a stronger computer tell me if this is a win or a draw? Thank you.

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