It doesn't matter to me how you define AST's gameplay aesthetic. The introduction of damage up card buffs back in 2015 was quite possibly the single worst decision that they've made for healing as a role. It's artificial 'utility', and it overshadows everything else you could offer as an alternative. As long as that is a part of your job, it's going to dominate your identity as a white mage with cards. Er, yes, I will use my mastery of the space-time continuum to... make your damage up buff last longer. That's not at all worthy of being called "time magic".
If you want a more nuanced support identity, then you need to make a clean break with the damage up buffs and start exploring other types of utility effects. I mean, this is what I would be asking if I was on WHM. AST gets to 'support' its team through damage buffs. WHM should get its own style of utility buffs. Let them give out Lucio-style movement speed boosts to melee dps to let them squeeze in extra GCDs before repositioning. Let them setup a Symmetra styled Warp Pad to let your ranged/casters jump between two points on the arena. Positional advantages translate into dps advantages in the hands of a good player. They're support effects, but it's not simple at all to evaluate their value. And that's the same type of design space that time magic has historically occupied in FF's history.
If you want it, you need to commit to it. Otherwise, let another support job do it the justice it deserves.