With minor changes, this is brilliant. I'd have Str. modify all damage, and melee to-hits. Dex. modifies missile to-hits and AC. Cha. should also modify some other things: Cleric undead-turning, opponents' save vs. any mind-affecting spell you cast, etc.
My reason for removing Strength is simplicity. All attacks get your dex bonus to the to hit roll. Simple. No questions. Damage is affect by Strength unless it is obvious that the user's strength is not involved: crossbows, guns, catapults, cannons, etc.
Undead turning is a sore spot with me. I'd probably do something simple like d8 per level of damage to one specific undead creature, once per creature. Or 1d6 per level of damage to a group of undead, hitting the lowest level undead creature first and carrying damage over to the next lowest undead creature until used up. This makes it formidable against a serious undead threat and against underling undead as it always was.
That said, what die would you use for initiative and surprise checks? Any modifier on a d6 is going to be *much* more relevant than on a d20.
I'd rather have it just modify the ability score - it's simpler.
d10. d6 was always too small and d20 was too big.
While working out an ExP progression for every possible multi-class combination would be useful, it's a lot of work that I'm not about to do.

(and I allow a lot more multi-class combinations than the RAW do). Also, I'd still like to keep the variable progression rate.
I think you misunderstood. There would be only a set number of charts 5, maybe 6. And each class and multiclass combo would refer to one of the charts: Cleric = B, Fighter = B, Mage = D, Thief = A, Cl/thf = C, Cl/ftr = D, ftr/thf = C, ftr/mu = E, etc. So you still have variable progression rates. They just aren't as arbitrary as 1e originally was.
Does nothing for me. I'd prefer that a weapon's actual rolled damage always be the same - thus, for a longsword you roll d8/d12 regardless what level you are. Messy otherwise, and asking players to book-keep their weapon damage at every level just wouldn't fly here.
Messy? I can understand not like effects based damage. But calling an effect that changes by level messy means you don't want 1e. Second, most people focus on 1e being a class system and ignore that it is a class and level system. I want level to have more meaning in my 1e. And weapon damage by class AND LEVEL is a great place to get it. A 7th level fighter is more formidable with ALL weapons than a 1st level fighter not only because he hits more often but because his hits are more dangerous.
Excellent. I'd like to see a third option somewhere between the two, however, and have that as the default; with these presented as rules-supported alternatives.
No, I'd rather have a really simplistic and a really complicated system and let everyone combine them however they like. Since the system supports the two extremely completely, any hybrid of the two should be equally supported. Supporting 3 system internally sounds wrought with difficulty.
Before getting too deep into this, we need to ask at what level the game will "cap out" at. If, like original 1e, it's going to cap out around 10th-12th, then only being able to cast 4th level spells by that point isn't much fun (particularly for Clerics, who really come into their own with their 5th-level spells). But if you think the redesign will remain playable well into the level-20's, then the slower spell gain is a good idea.
My experience with 1e never stopped at 10th-12th level. In fact, we usually started at 20,000 xp (around 4th-5th level depending on class/multiclass combo) and stopped in the teens. Adventuring with 6th-8th level spells in play is a lot of fun that I continue to be surprised by how many people avoided it when reading threads about 1e here and elsewhere on the net.
For the record, I would have there be levels 1-36 like in BECMI and move name level to 15th level. The details would be in the spells and monsters and I'm not going to go too deeply into that. (Name level: This is of course the spot where owning castles comes into play as an option in the DMG. I always hated that stuff being in the PHB.)
Clerics having books as well I'm not a fan of. They get their power straight from the divine. Also, I'd prefer to see pre-memorization done away with for all casters - the 3e designers really stumbled on to something good when they dreamed up the Sorcerer: all casters should work this way.
No real need to mess with them, I'd say; some minor tweaking to the tables and other than that 1e already has it pretty well nailed.
Here I'm torn. If I'm rewriting D&D completely, I'd nick Monte Cooks Arcana Unearthed spell system which combines preparation and spontaneous spell casting into a coherent whole which I wish he had come up with 5-6 years sooner and had made it the default for 3e.
Clerics are annoying on so many levels. I can imagine a whole pantheon of bureaucratic deities that will not lift a finger to help their clerics if the forget to bow at precisely a 37 degree angle when casting a spell and as such clerics of that religion carry around prayer books so that they don't make even the slightest error when casting a prayer. I can also imagine a deity with only one 5th level cleric who will show up at the drop of a hat to do anything to keep that cleric alive. Between these extremes there are many kinds of deities and many levels of strictness to their requirements for clerics to cast spells. I picked the most restrictive method because it mirrors the wizard's method of prepping spells and is therefore somewhat more balanced. That makes it a great default. DMs are free to lift these restrictions however they like.