When you get phantom paper jams, it's likely that one of the sensor flags is damaged or binding. We encountered a similar problem which turned out to be a physically broken drum/paper heater exit sensor, except the paper generally came out farther than yours is doing.
First I would make sure that the rapid release guide underneath the exit cover is properly seated.
Then check to make sure that the paper exit/tray full flag is not binding. It's on a shaft mounted at the rear of the exit cover. It's known to warp and cause problems.
With the exit cover opened, check that the tranfix exit flag is okay. It's located near the center of the printer around the rapid release guide.
There are more sensors on the circuit board on the upper feed roller assembly but they may be hard to see and get at. So if you haven't located the problem yet, I would get into diagnostic mode (pressing the "cancel" and "OK" buttons on the control panel) and navigate to the monitor sensors function. Now you can manually activate any sensor and the display will indicate its state (on/off). Try manually feeding a sheet of paper through the upper feed roller to verify that the various sensors are triggered.
In our case the problem was that the heater exit sensor was not returning to its off position. If you suspect that this sensor is the problem, you'll have to remove a few things to get to it, but you might first try gently tugging on the wires that go to it to see if anything changes. They enter the left frame near the top and front of the frame, along with the wires for the process and y-axis motors.
There may be an easier way to gain access to it, but I believe I removed the heater, which entailed removing the maintenance drawer guides, duplex guide, and upper feed roller assembly.
If you do find a broken sensor, gluing it back together should work fine.
Good luck.