I've been thinking about this further and come up with a proposal (in addition to the observation that 2 first level spells at level 1 is too much for the half-casters and they should get only one).
Warlock recharge other than on a long rest should only kick in at third level and be a feature of the subclass. This also allows you to actually transform the warlock's magic and have them give up pact magic for more orthodox casting while keeping the character entirely coherent even if the class looks a little odd; the character never actually gives up anything. And as can be seen from the above this (other than the first level slot) keeps the warlock in the sweet spot.
Suggested styles:
"Default" one slot proficiency times per day on a minute long ritual - example: Fiend Patron. This is intended to be a "middle of the road" warlock who's sacrificed for power. The Infernal Warlock has a ritual that takes a minute, and takes having either had Dark One's Blessing trigger since the last time you did this, sacrificing a tiny animal, or sacrificing 1d6 hit points to recover a spell slot. (The cost is meant to be trivial but thematic).
No slot recharge, but extra invocation-style magic - example: Great Old One Patron. This is for the warlock that wants to go all in to the invocations. They do weird things - for example an At Will Arms of Hadar (that scales). Your patron allows you to channel a bit of the Far Realms, and it's only the really big bits that take slots.
1-2 Full Recharges - example: Celestial Patron. You need more meditation - for example five minutes for a full recharge and your recharge takes concentration (purposely to interfere with Hex). It's a contrast to the Fiend and gives you less granular casting, for the old school but may be unnecessary.
Additional partial casting - example: Genie patron. You're a magical cheat who gets by with your sugar daddy's help. You don't actually do the foundations but throw your credit card at problems so you've the big stuff but are shaky with the little stuff, and you don't get a recharge. You get your low level slots on the Arcane Trickster progression (which flows naturally when you hit level 3, moving from 2 first level to 2 second level and 2 first). This can get pretty close to the 3.5 Warlock where just about everything was invocations and Eldritch Blast.
Transformative Full Casting - example: Archfey patron. What you traded for was knowledge and a teacher. You could never have found a wizard in the mortal realm to teach you, but you were able to take a risk and decipher enough of a ritual to have one of the Archfey to teach you (probably with the help of your Pact Boon). Your pact magic and arcane casting get rolled into your new full caster progression, and your other abilities from your pact boons are notably weak because full casting plus Invocations and Eldritch Blast is a really effective combination.
Transformative Partial Casting - example: Hexblade. You didn't want to become a caster. You wanted to become a Gish. You wanted your body empowered and the sweet magic weapons or blasts. This again doesn't feel disjoint because at level 3 you move from 2 first level spells to 3 first level spells. It basically puts you somewhere near the current playtest warlock but you can then work in more buffs so it gets either to a ranger level baseline and/or the spikes it needs (I'd suggest starting with shields and two handed weapons). And possibly a minor tweak to Mystic Arcana.
So everyone gets something of everything. I'd be excited to play the Fiend and Great Old One in this model. I'm not sure both Genie and Archfey are needed; whether the thematic difference I'm creating here feels meaningful enough. It also feels as if the old Vestige warlock can return under this model.
Also re: Mystic Arcanum as an invocation I don't hate it if and only if the warlock gets four more high level invocations to compensate. As it stands this is a savage nerf to the high level warlock and spell-locked Mystic Arcana slots aren't a match for the flexibility of high level casting. (And I would be more than fine with the Archfey having to spend four invocations to unlock their 6th-9th slots).