A few suggestions -
Shorten the depth of your dip a little and make sure your hips stay under your shoulders. Right now you're letting the hips move backward slightly and your chest drop. That immediately shifts your weight forward and sets you up to drive the bar forward.
When you drive, think of pushing the bar not just up but slightly backward - this is what Javier was saying - push the bar back over the back of your neck, not straight up.
Keep your chest back as you drive and split - don't reach your head and chest through so soon or as much. Let your chest and head move into position naturally with the effort to move the bar over the back of your neck. Trying to do it the other way (i.e. reach the chest and head) just pushes everything forward, which is another reason you end up in that bad split position with the bar too far forward to support.
Because your push press sounds good, try doing a push press + split jerk - likely you are good at driving the push press properly, i.e. staying upright and balanced and pushing the bar up and back, so this should help you replicated that in the jerk.
You can also try power jerks to help train that more upright and balanced dip/drive and bar placement.