Anthony Hopkins stars as a priest, performing an exorcism, in a scene from the 2010 movie “The Rite.” (CNS photo/Warner Bros.)

As member of the College of Bishops, whose unity with the Successor of Saint Peter is essential to its proper function in the Church for the accomplishment of the will of Christ, to continue His Salvific Mission on Earth, I hereby declare that I have examined the official Latin text of Pope Benedict XVI’s act of renunciation of February 11, 2013 A.,D., which begins with the words Non solum propter, and I have found that it is not in conformity with the requirement of Canon 332 §2, that states explicitly that a papal resignation only occurs when the Supreme Pontiff renounces the Petrine Munus.  Seeing that Pope Benedict renounced only the ministerium which he received from the hands of the Cardinals, and seeing that he did not invoke Canon 38 to derogate from the obligation to name of the office in a matter which violates the rights of all the Faithful of Christ, and even more so, of the members of the College of Bishops, to know who is and who is not the Successor of Saint Peter, and when and when not he has validly renounced his office, I declare out of the fullness of my apostolic duty and mission, which binds me to consider first of all the salvation of souls and the unity of the Church, that Pope Benedict XVI by the act expressed in Non Solum Propter never renounced the Papal Office and therefore has continued until this very day to be the one and sole and true and only Vicar of Jesus Christ and Successor of Saint Peter.  I therefore charge the College of Cardinals with gross negligence in the performance of their duties as expressed in Canon 359 and n. 37 of Universi Domini Gregis by proceeding in February and March of 2013 to the convocation and convening of a Conclave to elect Pope Benedict’s successor when there had not yet been consummated a legal sede vacante. And thus I do declare the Conclave of 2013 was uncanonically convoked, convened and consummated and that the election of Cardinal Jorge Mario Bergogio as Successor of Saint Peter is null and void and irritus by the laws themselves of Holy Mother Church, as established by Pope John Paul II.

An antipope is judged by anyone.

Antipope: A false claimant of the Holy See in opposition to a pontiff canonically elected. At various times in the history of the Church illegal pretenders to the Papal Chair have arisen, and frequently exercised pontifical functions in defiance of the true occupant.…
entry “Antipope,” Catholic Encyclopedia, 1913 edition


There are three lines of evidence that Bergoglio cannot be a true Pope:
his heresies before and after the conclave
his canonical disqualification for pre-conclave lobbying
Ratzinger’s invalid renunciation of the Papacy. There cannot be two living Popes.

Presuming #3 is not true, #1 and #2 would not be an impediment to +Francis' election, per Pius XII's conclave changes.  Manifest heresy and lobbying prior to the conclave would incur ecclesiastical penalties but such would be temporarily suspended for the election process.
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So +Francis would hold the human office of pope, but I agree that he is not a "true" pope, in the sense that he has spiritual authority.

But wasn't it JP2 who made the rules about lobbying for the papacy rendering the election illegitimate?

If you accept cuм ex Apostolatus Officio as law, nobody after Pope Pius XII was Pope (#1, so #2 & #3 are made moot.)