What is theologoumena?
We cannot be of one faith if there is a shadow of a doubt that dual procession is somehow detrimental to the Monarchy of the Father and, even to the Divine Economy.
Of course. That is precisely what needs to be clarified, that the dual procession is of the root-branch-fruit order, not of any other kind.
If "theological hypothesis" can be understood as mere theological opinion then I suppose it's probably the same thing, although I am not sure how it is treated canonically in the modern Roman Catholic Church.
Somehow, a hypothesis seems a step above an opinion, but I may be splitting hairs. It's just that it sounds more "scientific."
Faith is not an opinion, and I am not sure where such constructs fit in. They are either right or wrong and that is determined by the Church as a whole (Ecumenical Council).
But, apparently, the Fathers have had various opinions on a variety of issues -- some being perfectly orthodox, while other proved to be heresies. Others, yet, were rejected by the Church in whole or in part (i.e. Augustinian "original sin") without affecting the particular Father's standing in the Church (Blessed Augustine is a saint in the Orthodox Church as well).
As I said earlier, there is a certain amount of flexibility within the orthodox doctrine, inside whose boundaries these opinions remain just that -- unproven opinions, which are allowed, but are never to be confused as Church teaching.