I gave you a written proof with Tsunade herself and you still try tofind a way to move the goal post, really Atheck ?
No, you gave me an old rehashed picture from a notorious poster on Narutobase who persists in clinging onto that vocal tidbit as though it were a lifeline.
Okay I will show you evidence in story then 
Okay, I'll respond in kind to find which actually fits criteria and what doesn't.
If KIshi didn't bother showing her regenerating limbs it's not my fault but in the fight against Kabuto she regenerated
-a impaled heart
You mean Orochimaru damaged the general area where Tsunade's heart is. Kabuto only inflicted internal damage on Tsunade using chakra scalpels. He admitted that one could not be maintained during active combat long enough to drive it through into the deepest recesses of the human body.
By the way, just putting this into perspective, the human heart is roughly the size of a fist. A longsword's general width can reach over 4 centimetres. I doubt Kusanagi has those dimensions. Furthermore, healing a perforated heart is not the same as regenerating a completely new one.
-sword to her side and shoulder
Some lacerations are not the equivalent to creating a new hip and shoulder from regeneration. Tsunade managed to heal a penetration wound that went all of the way through Naruto's hand using Mystical Palm. It's nothing impressive.
-chakra scalpel damage
Congratulations, Tsunade counteracted some respiratory and thigh muscle injuries with Mystical Palm. You can't establish some equivalency to generating entirely new organs with that.
she also tanked a few moves that Madara did
This panel shows she can regenerate internal organs
Tanking hits that inflict nondescript damage says little about her restorative vitality, just her endurance.
Now, we don't have Tsunade regenerating limbs but we have Madara doing it, while in human form
I'm sorry? No, he did not. Your first panel only corroborates what I've been previously stating how the Byakugou and Hashirama's Sage Mode are similar enough in properties to be comparable with each other. The second contradicts what you've been trying to substantiate by Madara extracting another person's arm to use as his own instead of regenerating an entirely new one.
Going by this, I can say that if Tsunade or Sakura managed to obtain her lost body part she could at least "glue" it again
That's a feasible course of action, assuming Sasuke doesn't trim it down to mangled bits of blood, bone, and flesh or use the more sensible strategy which is scorch it until it's little more than blackened matter.
So yeah, I think you are trying to underminethe byakugou
No, I just don't interpret statements literally made when they're little more than unsupportable bravado.
About the Kirin situation...
And it was not only just two fire justu used, Sasuke used the Housenka, afterwards and Itachi used the Amaterasu ( a really big Fire justu), I doubt just two fire jutsu would be able to to make the atmosphere change enough for the use of Kirin
It's science

The multi-projectile Katon is the second one from Sasuke used in that battle. I took it into account. What you seemed to overlook was the fact that most of those jutsu were intentionally aimed at damaging the opponent. Sasuke's last Katon pierced the coverage of clouds to produce moisture through convection. If necessary, I'm sure he can unleash several more Katons of a greater intensity with more chakra to hasten the gathering of precipitation and lightning.
Besides as Sasuke himself said, it's his last resort and he basically does when he is chakra depleted
A last resort that he won't resort to if Tsunade somehow survives being sliced open multiple times?