Place a component on specific height above the PCB
If you stick with the surface mount connector and want to keep it's location then another small PCB is really your only option. The board could resemble a breakout board with 0.1in headers (or the like) on either side allowing the height of the board to change.

Your only other real solution without spending extra money is to move the connector. Turn the connector 90 degrees. Push the connector back.