There's one option you're forgetting: A support tool that contributes flat potency instead of a % DPS increase. I've been working on fully detailed redesigns of the healers and throwing ideas around, even on this forum, but I haven't fully set on what I think works nicely for Astrologian, but here's the basic premise I'm been trying to work with...
First, we take power away from Malefic spells. At the moment, Malefic IV is 250 potency... let's drop it to 150. Now, we add a GCD spell that deals an additional 50 Potency DPS whenever the wearer of the buff performs a GCD action. The target is the nearest enemy, or the initial target of the wearer's action if that target is an enemy. The buff lasts for 15 seconds. This potency acts as a separate source of damage. You can think of it like you're setting a star to orbit around your ally. You could also apply it to yourself when soloing.
The tricky part is finding a way to have this effect get applied dynamically so that AST players wouldn't just be spamming it on each individual party member. Perhaps it's a tool that heals the recipient of your card effects and applies this orbiting DPS star. This would compliment a rework of the cards to be all defensive utility since it lets you apply a damage buff to who you give a card too that also doesn't go to waste necessarily on Tanks or Healers.
Perhaps in a build like this, Time Dilation can exist as a GCD action with a 10 second cooldown, allowing you to try and keep up a card effect on one person? It's a rough idea to be sure. To make sure it worked, I'd throw it around during a table meeting with the other combat designers and just mess around with the idea. Sometimes the best solutions come from someone going "what if we did this?" And everyone just pretends it's happening for 30 minutes and just talks about it.
EDIT: I also agree that Lord of Crowns should be a burst of DPS. I imagine reworking Minor Arcana to not consume your normal card effects. Instead, you always pull Lord of Crowns and then alternate between it and Lady of Crowns as an oGCD heal to remove the random aspect. It will always change between one and the other, so you'll be able to plan for the Lady's heal while benefitting from the Lord's DPS