i completely get what your saying but we cannot assume kakashi wanst moving at his fastest speed because i saw kakashi bruised and battered from fighting hidan, ill say kakashi had the slight speed advantage but kakashi clealry had to be moving his fastest at that time because what shinobi or better yet what person is going to risk giving your opponent the chance to hit u when u knw if that opponent hits u there would be no way to when since all hidan needs is one scratch one drop of blood....
im sure she could keep up with hidan but she would lose to him because her speed isnt greater than his and she uses taijutsu and thats the absolutely wrong way for her to fight him because she would be opening herself up to get hit and then hidan would just start his ritual and kill her, her best bet is too summon katsuya and play defense instead of a direct assault like she is known for...
i dnt think tsunade knws hidans abilities, now if she does then she is very well capable of knowing all she has to do is remove the ritual circle but i dnt think she has intel on him but she might since she is the hokage but even still she could lose because knowing about something and actually facing it in live action is 2 different things....
Without intel she would not know taijutsu is not the way to do @ your second paragraph so she would do it anyways to start off, remember thinking as if there is no intel.
Even without knowing his abilities lets just say that because of this he gets her blood. She would be there as he draws the circle and then she realises she can feel the pain he does. She should be smart enough to deduce that the circle has a part to play and can shatter it.
Again that hidan getting her blood unknowing to him will not matter because she can tank it, she would activate byakugou as a safe measure from the time she sees when he is i nthat circle she feels the pain he feels.
she could even play dead(since he does not know what byakugou does without intel) and get him close and then use BPD (like she played dead against madara) and melt him after. Playing dead could work even if the circle is not gone cuz he would leave the circle and go to her assuming she is dead as he likes to offer his kills to jashin.
If he assumed she is already dead he would exit his voodoo form or w/e it is and revert back to normal.
or
After the circle is gone
she could engage him again and use BPD on him because once she gets close she can do it as we have seen the insane speed it worked for. Then katsuya can finish him with acid.
This is if she did not have intel. If she had intel I could see it going pretty much the same way by current feats. Except she would give him a wayy harder time to draw the circle in the first place.
I will be back later to check back, i have to go out.