Have you considered a 'convergence church'? They embrace the 'three streams of Christianity'. Here is an example:
The
Convergence Movement (also known as the
Paleo-orthodox Movement or
Ancient-Future Faith movement)
[1] is a
Protestant Christian movement that began during the
Fourth Great Awakening (1960–1980) in the
United States. It is largely a result of the
ecumenical movement.
[2] The Convergence Movement developed as a
syncretic movement among
evangelical and
charismatic churches in the United States blending charismatic worship with
liturgies from the
Book of Common Prayer, and other liturgical sources common to
Lutheranism,
Anglicanism,
Eastern Orthodoxy, and
Roman Catholicism.
[3][4][5] Denominational groups forming the Convergence Movement may self-identify as Convergence, paleo-orthodox, Ancient-Future Faith, or
Evangelical Episcopal; Convergence Christian denominations are often identified by the historic sacramental churches (and self-identified Convergence bodies) as some form of broader Anglicanism or Episcopalianism.
[6][7][8]
The pioneers of the Convergence Movement were seeking to restore a primitive form of Christianity different from what the
Restoration Movement taught.
[9] It was inspired by the spiritual pilgrimages of modern Protestant writers like Thomas Howard,
Robert E. Webber,
Peter E. Gillquist, and ancient Christian writers such as the
Church Fathers and their communities. These men, along with theologians, scripture scholars, and pastors in a number of
Protestant denominational traditions,
were calling Christians back to what they saw as their roots in the
early Church prior to the
Great Schism and rise of the
state church of the Roman Empire.
[10][11][12] Since the advent of Convergence Protestantism, numerous denominations and organizations have sought or claimed
apostolic succession.
As you see, they do believe their churches need to seek 'apostolic succession' which you now no longer embrace. If it is that much of a sticking point for you, then they are probably not for you. However, they are evangelical and charismatic friendly and reject prosperity gospel doctrines.
Navigating the "Three Streams" | The North American Anglican