That permadeath does not work is correct, the Brave Talisman they doggos have prevents that. You need Perfect Death. However, I still saw them revive sometimes and then there is still the red ninja girl... in cases like that you can just ragequit the run, as there seems to be no way to solve that, as attacks that apply perfect death usually deal damage and kill the dog and perfect death is not accounted for then. One of the new characters has a passive skill to apply perfect death, this might be the best solution, but I don't have that character and sofar I just farm madness.
You cannot grind for the cosmic shinobi, as there are no event soul frags dropping as rewards this time. Or do you just mean the grind for the 10 event souls?