I play against a friend of mine very regularly who mains Pyrrah, and after playing for months he's gotten very good at punishing Maxi.
My recommendation would be to counter this by basing your game on deception and timing. Base your game on 4b+k cancels, I started using it for the same reason you are having problems, your opponent can read Maxi. The flames are good for reducing that. I basically mix this up with three main components. Throws, 6a+b and pokes. If you stand in front of him and 4b+k cancel into 6a+b, JG can go frack itself, or throw, or step. Regarding the timing thing, there was an article about it on 8wayrun: Rhythm: The Death Drum. When you often flame cancel this becomes a stronger tactic. When your opponent is JG alot it means he is standing there looking for the hit. Pro players read so much, use this against them. Waiting for a long time before doing 6a+b is a classic counter fishing game that works against pro's. If they start getting the picture and poke you quickly, then just adjust and dont wait to long. In the end your strategy is safe, you can turtle and fish for counters while they feel they have to do something. Again, you have to implement flame cancel into your movement and aspects of your game for this to work in a cool way.
On a side note, I do use other moves, but they are situational.