I don’t hate the new Astro changes

[Seraphor]

Sleeve Draw's the one thing that'll make things difficult for AST, as that window is the most reliant on your comp and will mess up their seal management if you want to use it as efficiently as possible. If you have a standard 2/1/1 Melee Ranged Caster DPS split it 'should' be easy to just burn through it ignoring all your other tools, but non-standard comps can lose a lot of time to redraws without good rng.

Seals won't be an issue.
Minor Arcana is 1s recast. So if you don't need that seal, boost it to a Lord or Lady and grab the next one. No use for redraw.
So Sleeve draw just makes it easier, turning your 6 attempts into 8 for that Divination.

[Sebazy]

Seals won't be an issue.
Minor Arcana is 1s recast. So if you don't need that seal, boost it to a Lord or Lady and grab the next one. No use for redraw.
So Sleeve draw just makes it easier, turning your 6 attempts into 8 for that Divination.

^ This.

I can see the first priority being to ensure you are working towards getting your 3 seals covered in advance of the CD being up. Actually applying each card to the correct ranged or melee won't be quite so important until you're done with the seals and minor arcana'ing everything. If DNC ends up in the meta, throwing everything at the padded DPS when in doubt probably isn't going to cause any issues.

Another way to look at it is that the first draw is guaranteed to give us a seal we need. That leaves us with 10 draws (including redraw) to get 2 seals for the next CD, ideally it'd be best to get them within 8 (to ensure it's not late) which is where sleeve draw will likely come in.

[Grimoire-M]

Seals won't be an issue.
Minor Arcana is 1s recast. So if you don't need that seal, boost it to a Lord or Lady and grab the next one. No use for redraw.
So Sleeve draw just makes it easier, turning your 6 attempts into 8 for that Divination.

It has nothing to do with Minor Arcana. You want to use cards asap in order to make the most of the 3s recast time on Draw during Sleeve Draw's buff window. Spending time on Redraw/Minor Arcana during that window invites clipping or delaying it by additional GCDs, neither of which is ideal. The less you desync your draw timers the better, as Sleeve Draw can eat out a potential Draw or two if you don't use those cards asap.