1644 Papal Conclave double veto

So on the death of Urban VIII in 1644 the Cardinals gathered to elect his successor ultimately choosing Giovanni Battista Pamphilj who chose the name Innocent X. After the Franco-Barberini candidate, Giulio Sacchetti, was blocked by an exclusiva (veto) from the Spanish King the Barberini came around to Pamphilj (after some failed attempts at electing someone else and some bullying by the French). But Pamphilj was almost blocked by a French exclusiva as the Spanish had blocked the Sacchetti. So I am wondering how the election might have played out if Pamphilj had also been vetoed.

The Cardinals appointed by Urban VIII and loyal to his family, led in the Conclave by Cardinal Antonio Barberini, were the largest in number and had the support of Mazarin and the French Cardinals. But the Spanish lead by Cardinal Albornoz of course wielded the exclusiva. The French apparently wanted to back Altieri as a backup although a block of Barberini Cardinals unsuccessfully pushed Maculani for a time (who was opposed by a different block of Barberini Cardinals). But from what I've read the Spanish had no backup candidate and had no instructions from Madrid on how to proceed other that to back Pamphilj exclusively.

So if Pamphilj and Sacchetti are both vetoed is the French party able to eventually coalesce around Altieri and outmaneuver the rudderless Spanish to see him elected? Or would a compromise candidate be elected? First off the fate of the Barberini family hangs in the balance as OTL they underestimated the hostility Pamphilj would have for them once elected. But taking a broader view, Urban VIII had been a very pro-French Pope and his successor will have some influence on the settlement of the 30YW so a different outcome could have some profound effects.
 
Also a few alternate candidates I came up with;

Cennini, who was one of the oldest Cardinals, gathered about 20 votes in one of the scrutinies and early on there was some thought to electing an older Cardinal who wasn't appointed by Urban VIII. But he'd die OTL in the following year so another election would soon follow.

Facchinetti was apparently fairly well liked, and was even a papabile in one of the later elections though his time may not have come yet in 1644

Carpegna was nominally of the Barberini party but had a close attachment to the Medici family and Carlo de' Medici was the leader of the Spanish faction within the Curia. So maybe he could be a compromise candidate with a battle for influence ensuing between the Spanish via the Medici and the French through the Barberini.
 
What about Cesare Monti, Archibishop of Milan (50-years-old in 1644)?

A relative of Cardinal Federico Borromeo (Borromeo was probably the most important ecclesiastic family in Milan's history), he made a successful career in the Church before becoming one of most trusted collaborators of Cardinal Maffeo Barberini, who in 1623 was elected Pope as Urban VIII. Monti made a reputation as a skilled diplomat for delicate issues. In 1627 he became Papal Nuncio to Naples and in 1628 he was sent in Spain to work side by side with Papal Nuncio to Spain Giovanni Battista Pamphili to negotiate peace with Spain. Again successful, Monti replaced Pamphili as Nuncio when he was nominated Cardinal in 1630. Although some problems with the Spanish Court and his friendship with Pro-French Urban VIII, Monti had always a strong Pro-Spanish attitude. When in 1631 Borromeo died, Monti was nominated new Milan Archbishop after the previous nominee Girolamo Colonna was vetoed by King Philip IV of Spain. In 1634 he became a Cardinal and, as Archinishop and Nuncio, developed a strong collaboration with Spanish authorities, especially with the Spanish Governor of Milan, Cardinal Gil de Albornoz. As Archibishop he was noted for his morality, his support to organizations that assisted repented prostitutes and his efforts to mediate and protect the city during the wars between France and Spain. He was often called by Urban VIII as his envoy. In 1644 Conclave, loyal to his Pro-Spanish attitude, he supported his old collaborator Pamphili. When he died in 1650, he left the will to be buried in Concesa Sanctuary but was so beloved by Milan people that they refused and buried him in the Milan Cathedral. He left also a great art collection to the Diocese with the explicit prohibition to sell it.

So, if Frenchs vetoed Pamphili Monti seems a good alternative candidate-great person, Pro-Spanish Cardinal, good administrator, skilled diplomat and friend of Spanish Court- to replace Pamphili as nominee of Pro-Spanish faction and probably be elected before Frenchs can vetoed an other time
 
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