Hold on. When we're talking about traditional tridentine rites of ordination (or any tridentine sacrament) aren't those written/designed in such a way that the intention is PART of the prayer? In other words, as long as the bishop is valid, and matter/form (i.e. sacramental prayers) are said/valid, then his personal intention (or lack of one) is irrelevant, no?
Yes, I absolutely agree with this opinion. By performing the rite, the minister is doing WHAT the Church does. And the notion of "internal intention" is widely misinterpreted.
I use this analogy. I hold a loaded gun to someone's head, pull the trigger. Meanwhile, in my mind I'm saying, "I don't want him to die. I don't intend that he die." But by pulling the trigger you DID intend for him to die. Based on this warped definition of "formal intent," one would argue that he didn't really formally kill the person because he didn't intend for him to die. Of course he had the intent. When he willed and intended ("internally") the cause, then he also willed the effect.
You could have a Satanist priest up there saying, "I don't intend to transubstantiate. I don't intend to transubstantiate." but if he goes through and performs the Rite that the Church intends to effect transubstantiation, he certainly intended to do what the Church does, and the Church's intention for the effect is transubstantiation.
This warped notion of "formal" has also polluted some approaches to moral theology, such as regarding the jab. It's also been the root justification for EENS denial. But this concept has been abused and misapplied for the past few centuries.