The difficulty with proposing that supplied jurisdiction resolves the issue is that supplied jurisdiction is not habitual and doesn't give a person true possession of an ecclesiastical office. It's supplied to a person for particular actions at the moment it is needed. The person to whom it's supplied doesn't possess it any time before or after that.
Supplied jurisdiction does have a lasting effect, though the person exercising a juridical act under its terms didn't possess a lasting (or "habitual") jurisdiction. Picture someone coming to a priest without the necessary applicable "faculties" for confession and absolution. For the one act of the absolution the priest exercises a jurisdiction (supplied) which he dos not otherwise possess, and which disappears the moment the absolution is completed. However, for the penitent who was absolved, the forgiveness lasts, and the state of grace in his soul remains, exactly as with any confession and absolution, for however long he does not fall into serious sin.
It is one thing for a priest or bishop to be without any jurisdiction or faculties, such that every juridical act they do requires this momentary jurisdiction they can use but cannot keep. But if it were a matter of the jurisdiction being supplied for someone to appoint and ordain/consecrate a man to an office over some particular group of Catholics, the office once granted would be habitual, and its authority and jurisdiction habitual, even though the authority to confer it were supplied to the one granting it and disappeared upon the completion of that conferral.
So, just as the power to forgive the sin disappeared upon its forgiveness and absolution, the power to appoint and ordain/consecrate to an office might also disappear upon the completion of the conferral of that office, but the sin remains forgiven, and the office remains continually (or "habitually") held, and would only be lost through some subsequent legitimate act to remove the person or because of heresy or other resignation, even as the sin remains forgiven until a new sin is committed.
When Bp. Tissier de Mallerais wrote about supplied jurisdiction in connection with his apostolicity as a true bishop of the Church, this pertained, not to his individual juridical acts as a bishop (as if he were not in fact apostolic), but the jurisdiction by which Abp. Lefebvre and de Castro-Meyer consecrated him and made him one of the bishops over the SSPX, a perpetual and habitual office held by him. If there were no pope (as we sedevacantists already believe), then the right to have consecrated the bishops was absolute, legally speaking. But in the presence of one taken as "pope," and furthermore having to act against his apparent wishes (for John Paul II being in the state that he was could not be regarded as being "of sound mind and body" and was plainly acting against the good of the Church), this becomes a much more sticky legal situation - imagine having to prove in a court of law that John Paul II was not in a sane or right or papal state of mind when he refused permission to Abp. Lefebvre to consecrate the bishops, I think it could be done and would be right and just, but these things can be quite subjective and subject to a jury's whims - and hence quite properly a matter of "doubt of law or of fact." Supplied jurisdiction resolves this doubt in favor of the SSPX bishops, meaning that they are truly apostolic and possess habitual jurisdiction.