If you the production quantity is high, you can talk to the connector manufacturer and see what they suggest. They can use the same connector with different pins that act like stilts and place the connector higher, or they can custom mold a connector for you

The solution without spending extra money is to move the connector. Turn the connector 90 degrees. Push the connector back.

Some connectors have higher versions, and occasionally you can find a through hole mount connector where you can use a spacer underneath to place it slightly higher.

Very impressive posting. Thank you for your efforts.