Going back to my halfling cleric of Bahamut -- I RPed him casting Spiritual Weapon as summoning a dragon's head down to chomp on his foes (same damage die, of course). Is reskinning Spiritual Weapon to a natural weapon, such as a bite, acceptable, though, or is this spell restricted to summoning things that are of an archetype the wielder could hold in their hands? If it is restricted in this fashion, then what is Bahamut's favored weapon?
You can definitely make it look like a dragon's head. From the description of Spiritual Weapon:
The weapon can take whatever form you choose. Clerics of deities who are associated with a particular weapon (as St. Cuthbert is known for his mace and Thor for his hammer) make this spell’s effect resemble that weapon.
Bahamut isn't "associated with a particular weapon" (as far as I'm aware), so you can make your Spiritual Weapon look like whatever you want.