Are currently all ETH tx replayed in ETC by someone,..? If not, couldn't I just move my ETH to a address that I control and check if the coins move on ETC and if not move the ETC to a different address I control else repeat until ETH is moved and ETC remains.

As long as I do this with addresses I control that shouldn't pose any risk to my coins on both chains,.. right?
So if that's true and ETH tx don't get systematicaly replayed on ETC (where I see no incentive for) this would be a easier way to separate the two.