According to The Conciliar Anglican, the answer is to continue swimming in the Thames, rather than to swim across the Tiber or the Bosphorus. That is, classical Anglicanism is meritorious orthodoxy, arguably more orthodox than Roman or Eastern orthodoxies. The arguments are here, and I commend them. Especially commendable is Fr Jonathan's point that the filioque clause may not have been approved by the Ecumenical Councils but it expresses what Scripture teaches (note, in my view, especially Acts 2:33).
At Catholicity and Covenant, further reflections on these matters can be found, building on Fr Jonathan's post. One paragraph catching my eye is this:
"The Church cannot define dogmas which are not grounded both in Holy Scripture and in Holy Tradition, but has the power, particularly in Ecumenical Councils, to formulate the truths of the faith more exactly and precisely when the needs of the Church require it."
This is taken from the Moscow Agreed Statement (1976).
What, you might ask, is the difference between 'classical Anglicanism' and alternative expressions of Anglicanism? One formulation of the answer is that the former understands theology to be the formulating of the truths of the faith more exactly and precisely for the needs of the contemporary church while the latter understands theology to be the formulating of truths for the needs of the hour.
The problem with swimming the Thames today is that those 'truths' formulated for the needs of the present times have polluted the formerly pure waters forcing some swimmers to contemplate moving to waters perceived to be cleaner.
One reason I won't do that is some things in those other waters are uncongenial. One of them was celebrated yesterday by some Christians: the bodily assumption of Mary. Talk about a 'truth' not grounded in Scripture!!