Evolved Astrologian should take notes from Tetris
The original Tetris, like FFXIV's original AST, drew pieces completely at random, which led to a lot of frustration when the game refused to give you the most important piece. (The I-Tetrimino in Tetris, the Balance in FFXIV.)
Starting in 2001, Tetris solved this issue by putting the pieces in a 7-card deck that refills when empty. Every 7 pieces is guaranteed to contain exactly one of each piece. You might not have noticed this while playing; it still feels pretty random, even though it's much more consistent than before. It strikes a balance betwen the fun unpredictability of pure randomness and the fair reliability of a continuous repeating pattern.
My hope for Evolved AST is a system like this. Draws would be random again, but the drawn card would be removed from your 6-card deck until you've drawn them all.
This idea is already supported by AST's lore. I mean, it's cards. Why not make cards in this game work like cards in card games?