Belier's Bite and Natural Attacks

[Rands]

Trying to build a more effective Beastmorph Alchemist (themed, not hugely min/maxed), and trying to work in Belier's Bite with Feral Mutagen for flavour more than anything else.

I understand the difference between unarmed and natural attacks, but just wanted to confirm that my reading of the rules for Feral Combat Training is correct in this scenario:-

Level 1 Belier's Bite and Improved Unarmed Strike feats
Level 2 Feral Mutagen for the 1 bite and 2 claw attacks
Level 3 Weapon Focus (claws)feat for a +1 to hit with claws
Level 5 Feral Combat Training feat (claws) - IMPORTANT BIT - does this allow me to add the effects of Belier's Bite to the 2 claw attacks?

FCT description - Choose one of your natural weapons. While using the selected natural weapon, you can apply the effects of feats that have Improved Unarmed Strike as a prerequisite, as well as effects that augment an unarmed strike.

So when I use the Feral Mutagen (duration 10 mins/lvl) I end up with 2 claw attacks at DAM = 1d6 + 1d4 bleed EACH
and 1 bite at DAM = 1d8

1. Is this right?
2. Is there a better / quicker way to get the same effects? 5 levels to achieve a "theme" seems a bit of a heavy investment....

Cheers

[Reckless]

The bleeds won't stack. You just get the best you roll on the d4s.

Bleed: A creature that is taking bleed damage takes the listed amount of damage at the beginning of its turn. Bleeding can be stopped by a DC 15 Heal check or through the application of any spell that cures hit point damage (even if the bleed is ability damage). Some bleed effects cause ability damage or even ability drain. Bleed effects do not stack with each other unless they deal different kinds of damage. When two or more bleed effects deal the same kind of damage, take the worse effect. In this case, ability drain is worse than ability damage.

[Rands]

Reckless wrote:

The bleeds won't stack. You just get the best you roll on the d4s.

Bleed: A creature that is taking bleed damage takes the listed amount of damage at the beginning of its turn. Bleeding can be stopped by a DC 15 Heal check or through the application of any spell that cures hit point damage (even if the bleed is ability damage). Some bleed effects cause ability damage or even ability drain. Bleed effects do not stack with each other unless they deal different kinds of damage. When two or more bleed effects deal the same kind of damage, take the worse effect. In this case, ability drain is worse than ability damage.

Yep, that's not a problem.

But what about the bleed damage applying to the claw (natural attacks) via FCT? Is what I've outlined supported by the rules or have I misread CBT?

In my opinion, Belier's Bite would make more sense if it applied to both natural AND unarmed attacks from the start.....