I have trouble understanding the statement:
"Moreover, in my opinion something like two out of every three New Masses are already invalid, because the priests no longer believe in the Real Presence of Christ"
Does the priest have to believe in the real presence?
Yes, you are correct, and I've long objected to this spin on the NOM validity question.
Indeed, the priest only has to have the intention to do what the Church does, not to intend what the Church intends.
I guess the argument goes like this, though it's never been properly articulated. In the Tridentine Rite, the intention for the Holy Sacrifice is clear, and so in that case a priest who intends to do what the Church does thereby, via some transitive connection, implicitly intends the Holy Sacrifice. Meanwhile, in the NOM, the intention of the Rite itself is ambiguous, so it somehow has to be "supplied" by the active intention of the priest to intend the Holy Sacrifice of the Mass. So the principle here appears to be that with the NOM, the priest's must intend to do what the Church has Traditionally intended by the Mass in order to supply the absence of this intention of the Rite. This is extremely novel, and IMO a bunch of nonsense. If you read Pope Leo XIII on the Anglican Orders, there's no indication there whatsoever that the defective intention of the Rite could be somehow supplied for by the intention of the priest. He declared them simply invalid. Period. He did not equivocate about, well, if the minister intended to do what the Church intends by Holy Orders, it could be valid. He just declared them invalid due to the defective intention of the Rite. He did not say that each individual case must be investigated, to determine what the minister intended when performing the Ordination.
So you are correct that this approach to the validity of the NOM is completely novel and contrary to Traditional Catholic sacramental theology.
Nor does it take into account the problem with the validity of the Orders of the priest offering them. If there's positive doubt about the validity of the Holy Orders, which there has to be if Bishop Williamson conditionally consecrated +Vigano (who was "consecrated" originally by Wojtyla the Great himself), then all NOMs must be presumed invalid in the practical order and therefore no one an licitly approach to receive Holy Communion at the NOM (contrary to his infamous advice to the one lady that created an uproar). Either there is a positive doubt or there isn't. If there is, the NOM "Sacraments" must be avoided (teaching of the Church). If there isn't, it's not licit to conditionally ordain or consecrate. It's really that simple. But even Bishop Williamson and the pre- +Fellay SSPX have long muddied the waters.
Of course, how can anyone "investigate" whether the priest had the right "internal intention" anyway, since that's knowable only in the internal forum?
SSPX approach to the validity of the NOM "Sacraments" has long been a hot mess. While Bishop Williamson rightly points out that SSPX have refused to consider the possibility they might be invalid for political reasons, it's also true that the SSPX have engaged historically in the same refusal to consider them objectively in positive doubt due to also to the political reason of constantly having to fend off the evil specter that is sedevacantism.