Biting and Clawing the way to victory, getting the most natural weapon attacks? (2014)

I am trying to do some less optimized, but still powerful enough builds for high-power level campaign(s). Also, I have some dyslexia and want to make sure I'm not totally messing up my comprehension of what I'm reading. Would be a bit of a MAD build, but partially alleviated by the access to Gauntlets of Ogre Strength, and Belts of Giant Strength.

A while ago, with the release of Beast Barbarian, and now with The Predator patron from Humblewood, I got to thinking about making another attempt at melee martial with unarmed/natural weapons. Without using Monk.

Am I correct in my understanding of Beast Barbarian + The Predator can get 5 attacks per turn (not including reaction?) 
Beast Barb straight up adds an extra attack when making an attack with a Claw, and Predator can add 2 additional attacks after making a bite attack. 

Path of the Beast states Once, on each of your turns when you attack with A CLAW using the attack action, you can make one additional claw attack as part of the same action. So this is separate from the Extra Attack Feature.  So, that's +1 (and either Barb 5, or more likely, 5+ Warlock for Thirsting Blade.) Then Form of the Beast (Predator), at level 5 allows two claw attacks as a Bonus Action after making an attack with a Bite. Predator form also includes a BITE attack.

Now, I would have to get Hexshredder invocation (also from Humblewood,) to  make claws, that can be Pact Weapons, and Improved Pact Weapon (not 100% needed, but nice for the +1 bonus.) 

So, as a mono-class of either, it would be 4 attacks. But with both, its 5 attacks? I don't think I really give up to much in doing multiclass in this way. Raging as a Barb gives some bonus. As long as I dont have armor. I could technically still use a shield.  But overall, unless I'm missing a way to get some more unarmed/nat weapon attacks (again, excluding monk,) it looks like 5 per turn is the max, as Barblock? Also, excluding Haste. With the most significant downside being the setup - both Rage and Form of the Beast are BA. 

Its still a minimum of barb 3, Warlock 5, or barb 5, warlock 2. And I think Barb 3, Warlock 5+ is the far better option to also retain a bit of utility.  Ultimately, at level 20, it would be Barb 4/Warlock 16, or Barb 3/Warlock 17 of the last Mystic Arcanum is that important?

Applicable Feats (depending on luck with ability score rolls,) would be Focused Critical (Mage Hand Press), Vital Sacrifice (Critical Roll). And additional Invocations of: Lifedrinker, Eldritch Smite, Witch Sight, and One with Shadows in that order - after Hexshredder and Improved Pact Weapon.

I looked around, didn't see anything else that improves this build in terms of class/subclass features. Magic items beyond those that set Str, would be Wyrmwreaver Gauntlets from Bibgy Presents, and Insignia of Claws - unless I missed something else? Do Wraps of Unarmed Prowess work with Nat. weapons (claws?) They work with Unarmed strikes, but its unclear if that applies to Nat weapons.

Why are you dumping so much into Warlock if you intend to Rage as a barbarian? You can't cast spells or concentrate on a spell while raging, so most of your warlock levels are being wasted. You'd be better off investing into Barbarian to up your Rage-Bonus Damage, and so you have a reasonable number of Rages per day as at high levels you'll typically have 3-5 combats per adventuring day. If you aren't intending to Rage, then why take any Barbarian levels?

In terms of Class / Subclass features, three levels of Fighter for Champion gives you the increased crit range which combined with Reckless from Barbarian means you should be Criting every turn.

There is also the Order of the Lycanthrope Bloodhunter which deals good damage combining natural weapons with their Crimson Rite bonus damage. A Beast Barbarian-5 + Order of the Lycanthrope Blood hunter -3 is making 4 claw attacks per turn with +1d6 and +2 damage added on top of the base damage of each of those claw attacks.

As for magic items you'd want the highest level of Belt of Giant Strength and the Cape of Enlargement, potentially the Gauntlets of Flaming Fury.

Lifedrinker really strong, requires warlock 12.

But thanks for not reading what I wrote about number of attacks.