For the DPS cards:
Keep in mind that the three dps effects you chose would set in stone the best targets you have the moment you create the party and will lead to the "post your stats" meta. The 10% crit buff will be competely worthless if I'm running a min-crit BLM. You would have to know the stats of your party members to make good use of the cards.
Additionally, as the expansion progresses and crit becomes more impactful, the other two cards will become weaker in comparison, leading to the same "not Balance, sadface" feeling you had in Stormblood.
I understand that you chose this for diversity. But in terms of target choice for optimization and overall gameplay, the raw damage increase we have now is better.
Let's say you want/need one of the Umbral cards for mitigation. You have 33% chance to get the one you want. Your currency is dps and you're paying for a chance to gamble for a card that may or may not be useful to you. The issue with your Umbral cards (and old AST support cards) is that they are random, therefore unreliable, and probably too weak. I don't know why you chose a 15s duration for Umbral Cards.
A defensive card can be a dps increase if it results in extra dps gcds for the healers. But due to the unreliability, this will never be "a thing". Balancing this system would be a nightmare, which is most likely one of the reasons why they changed it in the first place.
You're going to have this problem on any system that has a dps vs support dichotomy coupled with randomness.
I do like your Astral/Umbral split idea, but the way I'd prefer it is by keeping the melee vs ranged dichotomy we have now and having the Minor Arcanas be the support cards. The default would be dps cards with a melee vs ranged dichotomy and an option for support cards. The support cards would have to be very strong ("save healing gcds" strong) in order for them to be used over the basic dps cards you draw every 30 sec. In other words, put the randomness into the dps cards and the reliability into the support cards.