I spent almost 10 minutes looking all this up. So I will make a statement, and then everyone can disagree.
Nothing new has ever been started in the Body of Christ (including these movements in the OP, Christian TV, and this website), other than by the mechanism in I Cor. 12:28. Understood correctly, in each case, we have seen the action, in order, of apostle, prophet, teacher, works of power, etc. Most people do not recognize the operation when they see it. This is because many churches have found it easier to teach that these ministries are not operative. The teaching became so pervasive during the middle ages that the definitions were forgotten, but are slowly being rediscovered now (hence the movements). This means that our whole definition of ministry and fitness for ministry is flawed, cessationism is simply factually untrue, dispensationalism is our imagination (other the second coming and those specific related events, which includes the return of the Jews to Israel, God has treated us the same since 33AD), we create the appearance of new relationships with God by how we organize ourselves to refuse certain things He has given us.
I think that covers them all.