Where did you buy the cards from? 'Cuz I'd be suspecting that they just might be counterfeits....
How Canon handles that... speculative, but... its not unreasonable to think they take it into account, and vary the actual synch in relation to the 2nd curtain movement, based on the predicted flash firing time (not HSS).
Either by way of direct mounting, or coupled external flash (cable, wireless), there needs to be an TTL flash "known" by the camera.
Moving from the 600D to the 5D3 will convert your current "112-320mm" lens into a 70-200mm lens, due to going from 1.6x crop to FF.
Agree. The change to a FF body is going to change your field of view significantly (like removing a teleconverter). On a FF body, your 70-200 will become a very versatile and effective portrait lens indoor and out.
For longer reach, I would recommend a 300mm f2.8 L IS and a 1.4x II teleconverter. The 300 will capture back the focal length you lose changing to the FF body while maintaining your 2.8 aperture. The 1.4x II will give you a 420 f4, fast and very accurate, especially when compared to the Sigma.
My work is in landscape photography, and I do not use (nor like) HDR---so digging shadows out is part of the normal work flow.