I'm a fan of using existing mechanical structures rather than (what I see as) reinventing the wheel. So what I'd do is elaborate on the existing Bull Rush, Grab and Escape rather than creating entirely new systems, and I wouldn't rush to create new modifier types.
The existing Grab from the PHB is a standard action Str vs Ref attack. That shouldn't be underpowered for someone with appropriate Strength - it's not a weapon attack so they don't get any proficiency bonus, but Fort/Ref/Will are typically a bit lower than AC, so on the whole it should be just as accurate as a normal attack.
You're right that Cha-based paladins and the like are poor at grabbing, in the same way that they're poor at opportunity attacks and everything else that uses basic attacks. Consider the feat Melee Training, which changes the ability score that basic attacks key off. Either create a feat like that for grabs, or simply rule that Melee Training applies to grabs too.
I didn't like that grappling in 3.5e provoked an opportunity attack, and I don't like it now. It discourages people from bothering.
Your approach, initiating a grapple as a minor action but requiring that weapons be sheathed first, is interesting but I suspect it doesn't quite work. Anyone who doesn't need a weapon to attack is unhindered by that demand, so for example, a monk or a Str-based cleric can still try to initiate a grapple and then make an attack anyway if they fail. (Or even a wizard, if they use Weapon Training to use their Int!) Besides, why do you need to be weaponless? A rogue grappling with a knife makes sense to me. (The original grab mechanics only require one hand free, so you can still hold something in the other hand.) So, I'd keep it as a standard action.
I'd also keep the original escape mechanic (move action, Acrobatics vs Ref or Athletics vs Fort). There's no real need to replace it. And after all, there are powers and magic items that improve your ability to make escape attempts, and those ought to apply to grapples as easily as grabs. In the same vein, if someone would gain a bonus to a grab or would be allowed to start a grab (some powers allow this), let it apply to grapples too. That's another reason I'd prefer to keep a grapple system based in grabbing - so that those bonuses carry across easily.
Of course, grabbing and grappling aren't exactly the same thing, because grappling is a two-way condition. So, changes you've suggested which make sense to me: the ability to use Fort instead of Ref as the defense (because hulking barbarians ought to be able to shrug off grapple attempts); grappling characters grant combat advantage; grappling characters can't do certain things.
On that subject - 4e's mechanics don't have any concept of "magic", let alone "stressful magic"; they simply rule that ranged or area attacks (of any type) provoke opportunity attacks, and melee and close attacks don't. Nevertheless, that works fairly well for what you wanted it to do. A grappling wizard shouldn't keep slinging Magic Missiles and Fireballs around, but he can still explode with fiery wrath by casting Burning Hands. And you can't keep firing your bow while you wrestle with someone.
You also banned the use of weapon powers. Sure, you shouldn't be able to swing around a greataxe or longsword. But like I hinted at above - if it were me, I'd let them use a weapon with the off-hand property (not a double weapon), like daggers, katars, and light war picks. I think that would work well for the most part. Although it would make sense to ban close attacks (rogue's Blinding Barrage, fighter's Sweeping Blow, etc.) even with those weapons. Personally I'd still allow melee attacks like Cleave, though.
So the actions that I'd ban while grappling: all ranged and area attacks, and weapon attacks except for melee attacks with weapons with the off-hand property. For this purpose, unarmed attacks have the off-hand property, and double weapons don't.
One thing I wouldn't keep from the original grab is the minor action to sustain it. Unlike grabbing, grappling is two-way. You don't want someone to escape a grapple for free by neglecting to sustain it. A grapple doesn't need to be sustained; it lasts until someone escapes.
What happens if a bystander inflicts forced movement on someone in a grapple?
I haven't yet looked in detail at the effects you're allowing grapple to have. I'll just post this now before I get ninja'd too much. And then I guess I'll spend the next hour editing, as is my wont.