Morphing Weapon

I was reading this thread, and have an answer to the last question asked: It might be possible to create a weapon that splits in two by creating a Morphing shield (enchanting the shield as a weapon) and a Morphing sword, and transforming each of them into one end of a double weapon.

This isn't strictly RAW -- that is to say, it isn't explicitly permitted by the description of Morphing. It's also not quite explicitly forbidden, although it requires a very, uh, creative reading of the property description (I'm using the MIC version). I personally would allow it because I don't see any significant advantage to be gained; it's cool but not obviously optimized or optimizable.

I have a question of my own, though. How would you rule a Morphing quarterstaff? The RAW on the ability says that if a morphing weapon is created as a double weapon, when it transforms into a single weapon it can use either side's bonuses.

Does this mean that only one side of the weapon needs to be enchanted with Morphing? Wouldn't that make it unable to change back if the non-Morphing side's bonuses were chosen (since the weapon in question would only have an 'inert' Morphing quality)?