No, they do not want to be with conciliar Rome - if that's what they wanted, they'd be with conciliar Rome.
I'm surprised to hear you say this Stubborn.
This is precisely what created the Resistance, the NeoSSPX wanting to be in bed with modernist Rome, which the Society had previously told us would be a betrayal of the Faith and the road to death.
Bishop Fellay put the Society definitively on a new course.
Never again was a distinction to be made between the Conciliar Church and the Catholic Church.
Conciliar sacraments were no longer to be held in doubt.
An extraordinary general chapter was held to make it possible for the SSPX to be controlled by Conciliar Rome with shameful conditions that are still in place today.
"Rome has asked that we criticise less and I agree", said Bishop Fellay, creating conditions of peace for an agreement.
All opponents in the SSPX and friendly communities were bludgeoned into submission in Stalinist fashion or expelled if they refused this new path.
Bishop Fellay continued rallying to Rome right until the end of his term. Who can forget his unbelievable description of a possible agreement under Pope Francis: "this cannot be a trap, it can only be friends wanting to do us good, wanting the spread of Tradition in the Church"?
Then Fr Pagliarani, the priest who saved Bishop Fellay's skin in the 2012 chapter, was elected to succeed him while Bishop Fellay and Fr Schmidberger, the two prominent accordists, had special positions created for them to manage the Society's dealings with Rome.
Fr Pagliarani himself approached Rome, evidently without success, in order to reopen dialogue. He also persecuted those associated with the Resistance. He brought Bishop Huonder into the Society with Pope Francis, and had him entombed beside the Archbishop as a perpetual monument to SSPX-Conciliar Rome relations and acceptance of the new sacraments. He has ignored all concerns from his priests and faithful regarding acceptance of the new sacraments. He has placed numerous Conciliar priests in the SSPX without convalidating their ordinations.
Never has the SSPX retraced its steps.If it does not have an agreement, it is not through lack of trying, but because Conciliar Rome is not yet ready, not yet convinced that it is the opportune moment to be able to destroy the Society. More time is required, more subtlety and re-conditioning in order to tame the big anti-revolutionary beast created by Archbishop Lefebvre.
It is not a case of "if that's what they wanted, they'd be with conciliar Rome".
Rather, it's a case of IF ALL OF A SUDDEN THAT'S NOT WHAT THEY WANT NOW, THEY'D SAY SO. THEY WOULD REPEAT THE WORDS OF THEIR FOUNDER "IT IS A STRICT DUTY FOR EVERY PRIEST WANTING TO REMAIN CATHOLIC TO SEPARATE HIMSELF FROM THIS CONCILIAR CHURCH FOR AS LONG AS IT DOES NOT REDISCOVER THE TRADITION OF THE CHURCH AND OF THE CATHOLIC FAITH". And if they don't say this now, in the current context, they will never say it. That should have us all very concerned about the future.
Kyrie eleison!