Towards the beak is OK, you could do that yes. That really would seem to be your only option aside from vetting or culling :/ You will have to get it back in somehow or it will swell and close off his airway. Somehow there is a hole right above the trachea passageway. The nares of his tongue have come through (those little forked pointy bits that help them swallow) and are more than likely what is keeping the tongue from going back in combined with swelling. Increasing the opening size would help. Does he seem to have feeling in the tongue itself? If you pinch the tip does he squirm and act like he feels it?
ETA:
To numb the tongue...oragel. It will numb any mucous membrane it touches. As much as it may hurt, try and squeeze the base of the tongue to get the points in.