Does anyone know if the Copper Idols (the Savannah building that allows you to swap base stat values) can be used on a neutered pet? Since the cost includes a breeding point, I wondered if unbreedable pets might be excluded. 

ETA: While I still don't know for sure about neutered pets (and would still welcome any sure knowledge!), I can now say that throdama morphs (also unbreedable) can definitely use the idols. 

Yes, it's possible to use the Copper Idols for neutered pets. However, the process still exhausts the life energy which is usually spent for breeding. So there's a limit for neutered pets too, and they won't be able to pay the price after a certain number of stat swaps (which is by a strange coincedence the same with their breeding limit if they were fertile).

Thank you!