My (theoretical) Path of the Beast Barbarian (lvl 3) Rune Knight Fighter (lvl 5) is already in a Rage (on a previous turn) and would like to use its claws (natural weapons) to make as many attacks as possible.
Fighting style: Two Weapon Fighting (adds modifier to off hand attacks, STR in this case)
Feat: Dual Wielder (ignores the "light" requirement for weapons, as natural weapons aren't light)
The character attacks with its claws (1d6+str+2), then, as part of the same action, it attacks with the claws again as part of the beast feature (1d6+str+2), then attacks again as an extra attack (1d6+str+2), then uses a bonus action to make an off hand attack (1d6+str+2), after that the character action surges and attacks again with the claws (1d6+str+2) and then again because of extra attack (1d6+str+2).
Assuming all the attacks hit, but no critical hits, that adds up to 6d6+6*str+12. If strength mod=+4, then this is a total of 6d6+36 damage, which averages about 57 in a round.
My question is, RAW can the character do this (have I interpreted all the rules correctly)? Does it depend on DM interpretation? Or did I just to the math wrong somewhere?