The point of worry seems to be a break in a succession of hands in ordination from the apostles who were the first followers of Christ. That strikes me as a professional historian of the Church (and also in Anglican orders) to be a very unrealistic view of Christian history.
First, ‘the historic episcopate’ throughout the Christian world is a pragmatic, gradual creation of the second century CE, which links with the first apostles, but does not do so exclusively. There was no single bishop of Rome, for instance, until the 2nd century, and earlier lines of single succession there are benevolent fictions.
Second, the Church of England is a Church of the Reformation which just happened to keep bishops. It is actually a ‘Reformed’ Protestant Church, that is not Lutheran, but part of a family of European Churches, some of which kept bishops in their government, some not. So national Reformed Churches in England, Ireland, Hungary, Romania and Poland have bishops. Up to 1662, clergy from other Reformed Churches served regardless in the CofE when they came here: often they were placed in English cathedrals or universities, not to quarantine them in some way but simply because they didn’t speak much English, and there they could exercise a ministry in the learned language of Latin.
In other words, never mind about that outdated Lambeth Quadrilateral.