(This is not for me)

Just curious.
Pre- Vll there were a few hundred annulments granted a year, and probably way more that were not granted.

Is there currently a way for a Traditional Catholic to at least attempt annulment proceedings, and if so, where?
Are current NO annulments legitimate? Were they in the past (sixties and seventies)? Since there is no juridical structure for annulments outside of Rome, is it impossible for a non-Ecclesia Dei Trad to get an annulment? Do they go to Rome (via Diocese), and if so, is that a bit hypocritical to do so?

Unless it's an "obvious" case, such as someone baptized Catholic who was not married before a Catholic priest, or it was found out that the person was still married to someone else, or something along those lines, I certainly wouldn't risk my soul on it.  This nonsense about not being psychologically prepared for marriage is certainly bogus ... anything that has any element of subjectivity.  If a marriage has deteriorated beyond repair, then just be content to separate.  People try to pretend that they have some inalienable God-given right to have intercourse.  It's as if you were married and your spouse was ill.  That's God's will for you, and you have to accept it.

In theory, you could go to the diocese in which you live.  One's standing with the Church, so far as I am aware, has no bearing on whether they will make judgment on an annulment or not.  In theory, a non-Catholic, or even a non-Christian, could go to the Church and ask for a judgment on their marriage or marriages.  All an annulment does is to say, in the eyes of the Catholic Church (and, as I always tell my son, thus in the Eyes of God), that a valid marriage does not exist.

For lack of canonical form annulments, so far as I am aware, pre-Vatican II and post-Vatican II norms are identical.  (I will stand corrected.)  I can't see that being a problem.

As far as often subtle and nebulous subjective psychological factors, obviously the traditional approach and the post-Vatican II approach are far different.  If one received an annulment on such basis, it would be up to their own conscience, whether to accept this judgment, or to say "these wouldn't have been traditional grounds, I cannot accept this annulment".

As far as the possibility of doing so outside of the diocesan structures, so far as I am aware, there is no way to have a marriage declared null.  I do know that, supposedly, Hutton Gibson declared Mel's marriage to Robyn invalid.  He had no authority to do this.