You just summarized the problem in the new rites...(1) the prayers/form no longer adequately provides the Church’s intention, so such intention must be provided by the minister. In the True Rite, the intention of the minister is irrelevant because the prayer/form perfectly says what the Church intends.
(2) Because the new rite NEEDS the intention of the minister to be valid, such intention is NECESSARILY INTERNAL because the prayer/form is too ambiguous and general. Thus, there is NO EXTERNAL SIGN THAT THE INTENTION IS INVALID (or valid), unless you can read minds.
So the new-sspx’s policy is neither grounded in reality nor logical. It’s also not consistent because it contradicts +Tissier’s past doubts on consexrations/ordinations.
I have to disagree. This intention theology is faulty and has been invented and propagated precisely in order to back up this notion that "even though we don't think the Rite is doubtful, we think there still may be doubt". That was so they could have their cake and eat it too. While putting it out there for public consumption (including by the Vatican "authorities") that, oh, no, there really isn't a doubt, they could still resolve their secret doubts by justifying the practice of conditional ordination. It was so as not to offend the Conciliar authorities. "Oh, no, it's not your Rite that's doubtful, really ..."
It is not required for the minister to intend the Sacramental effect, merely for the minister to DO what the Church does. That's why atheists can validly baptized. All they have to intend is, "I'm doing this thing that Catholics do." (and even that vaguely). They don't have to believe that it has any effect.
I had an SSPX priest who was conditionally ordained tell me that he himself had no doubts about his ordination, but he did it for "pastoral" reasons because a lot of the faithful at his chapel did have doubts. So he wanted to put THEIR consciences at ease.
See, I think the doubt theology evolved. Most early Traditionalists held the NO Rite to be doubtful in and of itself. So the SSPX used to do conditional ordinations without any kind of investigation or any requirement to demonstrate any reason for positive doubt, since the positive doubt was in the Rite itself. When this began to shift, to appease the Conciliarists, they came up with a new justification for continuing to do conditional ordinations (so the faithful wouldn't start leaving their chapels). So they came up with this "intention of the minister" problem to justify them. Well, as time went on, as LastTrad pointed out, fewer and fewer Traditional Catholics cared, so now they've stopped doing them altogether. That "intention of the minister" doubt is merely a negative doubt and it would require some positive doubt to establish whether or not conditional ordination would be licit in any particular case. Now they just don't bother anymore because they don't feel the need to.