Hello.
I'm afraid that your understand of the matter is not accurate.
Firstly, if you accept the term "full communion," then you would implicitly admit that there is such a thing as "partial communion," which would mean that schismatics and Protestants somehow have a share in the True Church while maintaining their rejection of the entirety of the Deposit of Faith. Full and partial communion are novel terms concocted at The Second Vatican Council. One is either Catholic, or is not.
Secondly: to state that the Society should sign a canonical "agreement" with Rome and should respect the Pope is both an oversimplification and a misleading statement.
The Archbishop, and the Society have always (and continue to do so) recognized and respected the reigning Pontiff. (Some may legitimately disagree on matters pertaining to post V2 popes.) If this were not the case, they would not have bothered to try to get permission to consecrate.
Furthermore, one does not negotiate with superiors. In a normal case, superior says, subject obeys.
The Council has demonstrably departed and ruptured from Sacred Tradition. I could provide proof of it in the council docuмents if you wish to study it for yourself.
That being said...in order for the Society to enjoy "full communion," it would have to accept the Council, it's errors, and the mass that it produced that outwardly displays the new theology and religion that it put forth from 1965-1969.
One may not do (or be silent.about) evil so that good may result. The end does not justify the means.
A father of a family would lose his right to be obeyed if he tried to force his children to eat a soup which, although mostly good, had a small or even trace amount of poison in it. (Principle of the integral good).
The goal is not merely to be recognized by the modernists...the goal is to preserve the faith. Faith before obedience. Authority exists only to guard and teach the faith. When it departs from the end for which it was established, it loses it's right to be obeyed.