A Fusion Fic would work way better than any kind of crossover.
Noble houses based on their powers, ie:
Starks have variations of the QA shard, they have powers that let them sense and control animals, much like the Greenseers in the original. Arya is now Skitter, you may panic.
Lanisters tend towards Thinker powers, Tywin has Number Man's power, which fits perfectly with his financial success and his cold and calculating outlook. Cersei with Accord's power? I mean, she's a conniving woman - and more than a little cray-cray.
Baratheons are Blasters like New Wave. Renly gets Glory Girl's powers, and Stanis is obviously Carol - amirite?
The Iron Born worship bloody Leviathan himself as their drowned god.
The Doom still rules Valyria - Behemoth loves to recline upon his Volcanic throne.
Entities = the Gods. We have two lone entities whose cycle is them competing against each other on every world they take. Planetos knows them as the Lord of Light and the Great Other. Except this type, they fucked up and their competition got out of control and caused way more damage than they were expecting, so they went into hibernation for a while: the first Long Night and the subsequent loss of 'magic'.
The Seven are similar to the Zion/Eden pair, each entity specialized in a certain area, all working together toward a common end.
Or maybe there are only the Lord of Light and the Great other and the other gods are just made up by people.