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The statement that each clock is moving slower than the other is just not true. There is no way to make an absolute statement about which clock is moving slower. Any statement is made within a specific frame of reference and is valid only for that frame.
NotReady, I think this snippet from RLK would be worth thinking on. Your perception that there is some paradox comes from assuming that there must be a state of affairs as to which is 'really' moving slower. As you allude to, your reason for thinking this is intuitive - it appears to us that time is invariant, that the speed of light will change based on how we move, etcetera. Same as your desk 'intuitively' appears solid, but is 'really' full of space.
To speculate in a hopefully useful way, I don't think SR is any threat to an absolute perspective - God's perspective or knowledge is from
every frame, in my opinion - not from one preferred frame (since such doesn't exist). He knows what everything looks like in every frame at every moment - the only problem with that arises if you consider God to have a present. A human habit, but not an appropriate one, in my view - since God made time I don't think it applies to him or restricts him the way having a present/past/future would.