The Death Ray can still be fired and the shields adjusted after the completion of the add-on storyline.
When looking out the window on the bridge you will notice 3 buttons to the left of the main button that fires the Death Ray in the quest This Galaxy Ain't Big Enough.... The further to the left you go, the higher the shield power goes up, but this also lowers the power of the Death Ray, and vice versa. The best strategy to destroy the enemy alien ship is to alternate between pushing the button on the right (providing maximum power to the Death Ray) to shoot, and pushing the button on the left (powering up the shield to max) when being fired upon by the enemy ship. That should make short work of the enemy ship, and thus end the final quest of the expansion.