The connectors for the Digitizer and LCD will never go in past the white line on an iPad. I've repaired many of them and they always either butt up directly with the connector to the line....or slightly before it. The headphone jack is a different story as I really haven't had a need to take too many of those out. Mostly see normal screen replacements. But
Heres a tip. There is usually a small section of slightly thicker plastic on top where the white line would be and right up to the tip of the connector. If you us a safe open pry tool or plastic spudger you can usually get a little better force on the connector without bending the cable. If you have neither, the corner of a credit card might work as well. It shouldn't take much force really (hence the name zero insertion force) But sometimes you need a little extra push to snug it into place.
If there is no going any farther without really getting into in, then there may be damage to the connector. Bent pins inside the socket or even damage to the connector itself (came out crooked or damaged with a tool)
Make sure you thoroughly inspect every part of it to make sure you aren't doing any further damage if something is bent or out of place.
Hope this helps!