A very interesting idea, and nice theme too.
EDIT: Is it possible this could be abusive to some cards, like SoG or other Shards?
It delays the permanent and gives you the ability to play a 7th+ copy.
So we should examine all permanents that have increasing returns.
Examples:
Dimensional Shield: 6
+ 1 card => 3 Turns each (capped at 18 turns)
Dimensional Shield Archive: 3
+ 6
=> 2 Turns each (no cap)
Sundial: 0
+ 1 card => 1 Turn each (capped at 6 turns)
Sundial Archive: 3
=> 1 Turn each (no cap)