How can I store my extra wheels on the wall efficiently, without hanging them by the rim?
While I agree that there are no real risks to string your wheels by the rim, there are a number of DIY and commercial wall mounted racks for hanging wheels at the axle.

Wheelzrack makes one good option, and even integrates a storage shelf for shoes and helmets. They support up to for sets of wheels, which may be a good option in your case.



Feedback sports used to offer a Wheel Arm system, which had a bolt-to-wall mounting option (note: the Wheel Arm is no longer listed on home page but they sell alternate models).  These are designd for shop displays, but will work in the home as well, assuming your significant other is tolerant. :-) 

Hope that is helpful.