Phoenix: Ok, let's follow your plan, which indeed looks like the only winning attempt.
Black obviously has to play a5 to get anywhere, as white has all the squares cut off from the enemy king along the fifth rank.
Black plays h4 to fix all of white's pawns on light squares.
Let's say after black moves ...a5, ...Kxa5, ...h4 black's king manages to penetrate to d2, and white's king is on f2. Outflanking is not possible here.
Also in this situation, if black tries to trap the knight hoping it runs out of moves, the knight has the e3, f1 (and from f1, h2 and g4 squares as well) and d5 (because with black's king on d2 taking the knight is not possible) squares available.
That only leaves pawn breaks.
And if ...f5 exf5 then that only leaves the ...e4 fxe4 break, and these exchanges aren't leading anywhere.
So black has no realistic winning chances in the final position.