Run into this problems many times. I believe it's mandated by the country for security reasons, one ID per room, so one ID/person cannot be living in 2 rooms at the same time (at the same property).

On check out, I usually ask the front desk to print out paper copies of each room bill with my name on them. Then retro claim.

Though with my stay at Le Meridien Shanghai, they transferred all the charges to one room, and somehow figured it out and gave the correct credits.

I've had the Westin Bund disclaiming me as a Plt member, so I can imagine what you went through with them! Not a fan of them, lot more choices now for SPG properties in Shanghai with much better locations and service.