Custom device with multiple gates tied together in Eagle
Am I missing something, or am I going to have to create a boring rectangle symbol with 12 pins for my FET array?


No, as far as I can tell, you are not missing anything. I asked myself the same question a while ago and went through the Eagle manual, which states:


  It is not possible to connect several pins with a common pad! 
  A  Device  may  contain more  pads  than  pins,  but  not the  other  way
  around!


(Manual Version 6 - 1st Edition - Page 243)

From eagles perspective it does not make a difference if there are several symbols involved or not, since the "Connect" dialog just lists all pins and pads anyway. I don't know if this was improved in Eagle 7.