You are posting in the wrong forum. That kind of question goes either in the Relativity forum or in the Cosmology forum. Maybe one of the staff will help get it in the right place, and the people there will answer and discuss with you.
(For starters: Just because distances between things increase according to an expansion pattern does not mean that space is moving. It doesn't even mean that the things themselves are moving in the ordinary sense so that special relativity time effects would apply. Approximately uniform distance expansion is not regular motion because it doesn't get you closer to anything. It doesn't fit the special rel picture. No motion effects on time. Try reading the beginning parts of the balloon model sticky thread in Cosmology. Might help.)
No more about this until your thread gets in the right forum. Doesn't belong here.