There are only two ways:
1. God's direct intervention.
2. The mechanism of the Church.
If #2, then in the absence of the Cardinals the power of election falls to the Roman Clergy and the hierarchy. These two bodies cannot in toto defect from the Faith and become extinct. If a Pope is to be elected, the electors must be from these two groups.
The Pope must also rule over the diocese of Rome, so some or at least one faithful Roman priest must submit to him.
I would like to add only one thing to what you have said. The hierarchy eligible to elect the pope includes those bishops and/or priests who do not currently have or claim to have jurisdiction. For example, Bishop Tissier claims to have apostolic succession (see May 2013 Catholic Family News) and I would agree with him. If he does have apostolic succession he is certainly a member of the Catholic hierarchy even if he does not currently claim any jurisdiction. Therefore he is eligible to elect a pope. It is a fact of history that even laymen have cast votes for legitimate/valid popes.
Has anyone contacted Bp. Tissier to confirm as a fact that he is now claiming apostolic succession?
The traditional bishops and priests other than those sent by the Church have no more power to act in the Church than you or I. They have orders, and use those orders, but no mission or authority, or any greater power than a layman. The traditional clergy have no legal status, and operate strictly by the request of the people for the sacraments, and supplied jurisdiction for confessions on a case by case basis.
Laypeople in the early Church may have voted, but it was the clergy of Rome that mattered. Without the acclamation of the Roman Clergy, a man cannot be Pope.