UPDATE: I have updated the OP with compiled lists for the BIG 3 (as I call them). For other contributors, if you have compiled (roughly completed?) lists, let me know and I will add links in the OP.
Wow, it looks really good when it's all laid out like that! I think the themes of the different lists come across really well now.
I know pretty much everyone will have different opinions as to the best way to modify classes to fit into the new paradigm, so I'll just throw my hat into the ring. Maybe provide some inspiration.
Cleric - Spells from Divine list, modify domains to only provide spells from the Divine list.
Druid - Spells from Primal list, modify any CIrcle spells to only be Primal spells.
Sorcerer - Spells from Arcane list. Divine Soul allows spells to be picked from Divine List instead of, not in addition to. Sorcerer points recharge on a short rest.
Wizard - Can learn spells from any spell list into their spell book. At 1st level, must pick 3 oppositional schools (necromancy, abjuration, etc.) that they cannot put into their spellbook.
Paladin - Spells from Divine list. Changed to spells known caster, progression as ranger.
Ranger - Spells from Primal list.
Warlock - Spells from Arcane list. Change to standard half-caster progression, spells known from Arcane list. Eldritch blast as class feature, 1 beam for 1d10+Cha at 1st, 2 beams at 5th, 3 beams at 11th. (I never liked how the 4th beam stepped on fighter's toes, and there isn't any damage cantrip progression anymore to compare with.) Invocations increased (1 extra at 3th, 7th, 10th, 13th, so 12 total at 20th level). Invocations that grant spells 1/long rest do not require a slot.
Bard - I'm struggling with bard. I like the "all list half-caster" symmetry, but it would also be in a good spot as a full caster with access to all Divination, Enchantment, Illusion only. Maybe extra magical secrets as well.