A poorly telegraphed ground pound and X-ray, along with the fact that his command grabs aren't really command grabs, are things that tick me off most about Jax, and probably the reason why you haven't seen one on a tourney stream. As far as I know, the ground pound can be used to duck projectiles, so you can throw it out if you sense one coming and then dash in follow up
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or whatever. Also, it's been said that Jax is an "in-your-face" kind of character, so assuming you're pressuring your opponent correctly, you can throw out a GP as they're turtling in anticipation of another block string assault.
But then again, I'm a scrub, so this may or may not be the best advice. But if you ask me, it seems to be the only way. Jax is gimmicky like that.