The 4th point of the Lambeth Quadrilateral affirms "The Historic Episcopate, locally adapted in the methods of its administration to the varying needs of the nations and peoples called of God into the Unity of His Church."
There is no mention of any other ordained ministries - priests or deacons. As an ecumenical challenge towards conversation for reunion this part of the Quadrilateral is both a difficult affirmation to understand and a difficult stumbling block to some conversations towards reunion.
I believe it was carefully crafted in order to open out two Anglican sensibilities for greater creative conversation. They concern the matter of continuity of laying on of hands - manual transmission - of the episcopate on the one hand and the question of the form of ministry of those the bishops and people call forth.
In its widest grasp the Lambeth Quadrilateral does not preclude communion with Churches who do not have unbroken manual transmission of orders. It does not preclude communion with churches that provide for sacraments and the preaching of the word in ways quite different from Anglican bodies.
The proposed Anglican Covenant expands the first affirmation of the Lambeth Quadrilateral with this phrase, "and to which the historic formularies of the Church of England bear significant witness." Among which formularies, of course, is the Ordinal, in which the three fold ministry of Bishops, Priests and Deacons is affirmed. Interestingly the Covenant does not say those historic formularies are essential, but that they bear significant witness.
The question is, if the Lambeth Quadrilateral does not mention priests and deacons, and the creeds do not, and if there is no mention of the necessity of manual transmission, what is to prevent our reunion with the African Methodist Episcopal Church without any "re-ordination" of their bishops, or the possibility that a Diocese or Province might assign presiding at the Eucharist in the absence of the Bishop to Deacons or Lay Persons? In particular, if the formularlies of the Church of England are considered "significant witness" but not binding?
Perhaps we need to honor the possibility the ecclesal and theological validity of Church life in which Bishops were ordered anew out of necessity, or churches where the sacraments are of such importance that presiding is ordered by the Bishop in ways "locally adapted."
Perhaps Sydney is locally right, although widely peculiar. Perhaps the Methodists are right more widely, although universally peculiar. After all Anglicans are peculiar as all get out.