Sure. For some reason I've become a bit obsessed with analyzing a game that I gave up on like 30 years ago, and which after trying to play several times since then decided never to play again. I don't know why that is what I'm hyper fixated on, but here we are.
In my case, it is defniitely fueled by nostalgia. Redesigning AD&D is a fun mental exercise : what changes could I could make that really improve the game while preserving its magic? Of course this judgment is purely subjective, but my personal AD&D is a game that I want to play (or DM).
Also I think you are maybe using B/X initiative and not realizing it.
So let's look at the actual rules. Please read this and get back to me about "cosmetic fixes".
Now, there is some of that I really like, including the part you called out as disliking. Absolutely in a charge situation, the person with the longer weapon should go first regardless of the initiative order. That's a great rule, and one I would keep. But the overall system is overly complex and involves way too much exception based design. That document had to be compiled from all over.
It's possible I'm defaulting to B/X somehow, but I rarely played it even as a teen. I did play Holmes.
I use most of the resolution methods in the consolidated document you shared, but I haven't felt the need to create detailed rulings for rare magic items, psionics, how to handle spectators, etc.
For multiple attacks during surprise segments, I have decided that simpler is better: one melee attack or missile attack per segment is plenty. Last year I also read obsessively all the perspectives offered on the Dragonsfoot forum, both for and against the triple rate of fire statement in the DMG.
I like the rule that longer weapons strike first when closing to melee range, but there are always exceptions and I think the real intent is for the DM to make a ruling based on their understanding of the situation. For example, if a spear-carrier is part of a shield wall facing the wrong way, or if the person closing to melee is a thief sneaking up for a backstab, then I would not necessarily give the spear the first strike. That's one example of why I consider some of the initiative chapter rulings and not rules.
The only initiative rule I actively dislike is the higher d6 roll going first and the pointless math shuffle it engenders to determine the starting segment of a prolonged action.
This is somewhat the opposite of where I would go. Getting more out of high ability scores makes the problem worse and makes the need to only play a character who has the right high ability scores greater.
In which case you'd be better off just agreeing on the array you wanted to use ahead of time. But I want to note, "everyone using a common array" is the height of not playing in a first edition style and is rather the opposite of claiming play what you get is a good thing. Your fix is a reversal of basically everything about character generation as it existed before 1985 or so.
That's fair, and the way you decide to handle ability scores has an impact on the style of game you want to promote. This is the single part of AD&D that I struggled with the most in my personal design.
A score of 15+ is not that rare in the population: about 10% on 3d6. About half of NPCs generated on 3d6 will have at least one score of 15 or better. About half of PCs generated on "4d6 drop 1" will have two scores of at least 15. From that mathematical perspective I decided that it was not unreasonable for mechanical bonuses to start appearing when a character is at the 90th percentile. (But again, where you want the bonuses to start appearing is a subjective choice--I'm just explaining the context that made me personally comfortable retaining the 15+ principle, mostly)
Does this make a game where the PCs tend to have high scores, and feel like it is necessary to have high scores? Absolutely. Does this make them more likely to survive and thrive? Somewhat. But having high scores does not make you invulnerable. Not even an 18 Con will help you if you find yourself stuck in the front line against a troop of orcs who are rolling well. Bad tactics and choices cause character death more quickly than any other factor!
Finally, you bring up the other aspect of "AD&D style" that I cannot abide--the dice lottery for PC creation. I want my players to feel like they can grow attached to their characters, and having unlucky rolls in character creation or leveling up can absolutely suck the joy out of the game. Not just ability scores, but hit points too! BUT I also want the ability score arrays to feel organic, not planned. So everyone at the table rolls their array on 4d6 drop one, and maybe Lucy has 16 15 15 11 10 8 while Ricky has 17 14 12 12 8 6. Some players who roll worse than either decide to use Lucy's array, others use Ricky's, and that's just fine with me. No one feels shortchanged. And for HP I give the maximum for the first hit die and half maximum for all subsequent hit dice.
I don't think this takes away any of the charm of a long-form campaign. Now personally, I would play in a meatgrinder AD&D campaign where PC death is expected early and often, and part of the fun is running multiple characters and seeing who survives. In this case no problem with fully random ability scores and hit points. But that is personal taste and I don't think most of my players would find that sort of game fun.