Sooo the matchup discussion was closed for some reason. There was some really good info in that thread too
But I've got another option vs Jax when you knock him down...If you dash up and use d4~clone you will be safe from all of his wakeups except ex dash punch. If timed correctly the clone will freeze him for a full combo if he uses Overhead smash. If he uses ex Overhead smash it will whiff and you'll be at advantage, if he does a wakeup gotcha your d4 will hit him out of it, and if he stays grounded you will recover from the whiffed d4 pretty quickly so you don't lose much advantage.
If Jax tries a regular wakeup dash punch I'm pretty sure you have time to punish it, but at the very least you'll be safe. Now if he starts using ex dash punch to stop this set up, you can use the d3~dash forward oki that I posted a while ago which can punish him for a full combo. Or if you dont want to take any risk you can just hang out at sweep distance to be safe from all his wakeups.
I've also been trying to incorporate RedRaptor's d4~clone trap recently with some success. I think there are certain situations that it can definitely be more effective than 212~clone