Three priests and one ex-priest whose allegations of sexual misconduct against the archbishop of St Andrews and Edinburgh, Cardinal Keith O'Brien, led to his resignation a year ago, have appealed directly to Pope Francis for a meeting in a last-ditch bid for justice.

Describing the church as a "formidable machine" that had blocked any investigation, one told the Observer: "The abuse we received at the hands of Keith O'Brien is dwarfed by the systematic abuse we have received from church officials. They have passed the buck, misrepresented the truth, engaged in cover-up and, having asked for our trust and co-operation, shamelessly procrastinated and hidden behind a veneer of diplomacy and charm. I want to ask Pope Francis, can you sort this out?"

Secret negotiations have been going on between the men and the cardinal's successor, Archbishop Leo Cushley, since last November. The archbishop insists that only Rome can initiate an inquiry into O'Brien's sexual behaviour, but he has agreed to an investigation of the cardinal's financial transactions. In an email to the complainants last December, the archbishop's vicar general, Philip Kerr, confirmed: "The archdiocesan auditors have been asked to examine the financial accounts which Keith O'Brien personally operated."

"Lenny", an ex-priest who rebuffed O'Brien's advances at a seminary, says that the diocese is a charity and he would have contacted the charity regulator if Cushley had refused the audit. "Keith O'Brien was essentially the CEO of a £9m charity. We want to assure ourselves that this institution is not totally corrupt."

The group know that the cardinal bought a priest friend a jet ski for his birthday. "Jet skis cost thousands of pounds. How can a man who was an archbishop have the money to pay for a jet ski for his pal? Catholics should not give a penny more until they know the church is spending it on something they intend to pay for."

The complainants tabled a formal paper at a meeting with Cushley in Edinburgh last November, repeating the need for a formal investigation and proposing a number of initiatives. These included a public apology for "the victims of O'Brien and all those affected by abuse throughout the church", but also an investigation into governance in the diocese. They wanted to know how O'Brien had come to be appointed, the extent of his predatory behaviour and whether those close to him had been manoeuvred into positions of power under his leadership.

Most damaging for the church was a request to examine potential sacramental abuse by O'Brien. The complainants have asked if the cardinal sought absolution in confession from anyone he had committed a sexual sin against. This offence is regarded as so serious that the penalty is automatic excommunication. In church eyes, any sacraments the cardinal had subsequently administered would be illicit.

Cushley, a former Vatican diplomat, insisted he could not take action independently, but would pass requests to the Vatican. He offered a private apology to the men for their suffering, but said a public apology required Rome's approval. A spokesman for the archbishop said: "Archbishop Cushley has listened to the parties concerned and will transmit any information to the Holy See. Any decision on further action will rest with the Holy See as jurisdiction in the matter rests with the pope."

For the four men, the last year has been traumatic. They have been accused of seeking vengeance, while Bishop Stephen Robson, a close friend of O'Brien, has called publicly for forgiveness for the cardinal. For those involved, such calls are simply another church mechanism to silence them. "Denial is deep," says one. "They are so lacking in compassion. Why have we been waiting so long?"

The Vatican ordered O'Brien to undertake an unspecified period of "prayer and penance". In recent months, however, he has sent out personal cards with a photograph of himself, still in his cardinal's red robes. It is, say the complainants, a sign of both his inability to confront his actions and the church's inability to deal with him. "Keith was power hungry," says one. "Now he is a wounded lion, but I'd like to see them remove his teeth and claws. That might mean removing his red hat."

Lenny said that the past year had cost him "physically and emotionally". Watching O'Brien's elevation led to his decision to leave the priesthood, costing him his vocation and a crisis of personal faith. He is now married.

But speaking out has had one positive effect. "It has been the most authentic decision of my life and I know my motive was not hatred. I have had a sense of God over the last year that I haven't had for a long time. I have felt a bit of a guiding presence."

Last week Archbishop Cushley travelled to Rome, assuring the complainants that their requests would be personally delivered. However, he suggested justice had a better chance if "discussion of the case in public is avoided".

"They always demand silence," says Lenny, "which is ironic given the church has been spinning relentlessly all year.""

In an email to Lenny, the archbishop wrote: "Please be assured that I will transmit your request for an audience with the Holy Father and the Secretary of State. As with all such requests, I warn you not to hold your breath for a reply, but you never know."

Lenny said: "If even Francis won't talk to victims of abuse because the abuser is a cardinal, then that will be disappointing – and very telling."