Big cube "Ortega"

Depends on what you call orienting. Of course "orienting" the wings will be nothing else than a permutation, but speaking of orientation makes sense for recognition's purpose.
 
Um, I am sorry, but this is an extremely bad idea. It won't be good for speed OR fewest moves. You need freedom in movement and this method has none; as soon as you make one layer you're dead in the water. And "permuting" a layer is an awful idea on anything above 3x3 because you can't do it in one step, so you should just solve pieces where they need to end up. This method sounds like solving the entire thing with commutators, except in a random order and moving a lot of pieces more than once.
 
I tried it and it was not any good, maybe after a long learning period with many cases.

For centers the orientation would be 1x2 blocks aligned in the same direction as the layers (horizontal) but in any of the layers and on any side as long as it is FRBL centers, U and D will be oriented as normally in up and down face (better to use RL for faces but for descriptiopn UD will do =).
 
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