He has weathered stormy seas since he invited a female minor canon into the ranks of St Paul's two years ago. And for many, the Reverend Lucy Winkett has come to symbolise the bitter feud over ordination which has recently divided the Church of England.
Traditionalists, furious that a woman priest should be welcomed into the fold of a such a high-profile place of worship, have vented their anger, and while outsiders have sent"crazy" hate-mail, insiders have threatened to walk out.
Throughout the turmoil in the cathedral, the dean has stood unflinchingly at the helm, in support of the 31-year-old Rev Winkett, saying she is an "outstanding" candidate who has his staff "united" behind her.
Yesterday, however, Dr Moses, 61, admitted there had been a lot of "pain", and he had been "shocked and saddened" at the vociferous opposition.
Tomorrow night Rev Winkett's pain will be laid bare as viewers of the BBC2 documentary St Paul's see her break down in tears. The young priest's obvious enthusiasm upon her five-year appointment to St Paul's has been eroded.
The cause was clear. Dissenters had stayed away to make their opposition obvious - a group of London diocesan clergy were noticeably absent at the cathedral's tercentenary celebrations. And colleagueshad voiced their displeasure; two senior colleagues, including Canon John Halliburton, had not accepted her authority, and, at one point, her staff servers refused to celebrate the Eucharist with her. "I don't want to be in this cathedral," she says in the documentary, "but I have to carry on." The programme was filmed over two years and runs to three 50-minute, fly-on-the-wall episodes.
Senior members of the London diocese have also opened criticised the dean. Dr Moses is adamant, however, that he was not playing "gender politics" when he appointed Rev Winkett - she was the best of 16 candidates, he says.
Publicly the dean has been careful to emphasise his respect for both camps in the battle of ordination, insisting they can "live together". But many felt he had nailed his colours to the mast by appointing Rev Winkett within months of taking over as dean. "I did not expect such controversy. Women had been appointed to more senior roles in other cathedrals," he says.
Since the first women were ordained five years ago, 2,000 have joined their ranks. A dozen have taken up cathedral positions and almost 800 are in charge of parishes.
But, in the minds of many, St Paul's was unique. "For some time she was in an isolated position in the sense that she was the first woman priest at St Paul's," says the dean. Of the harsh attacks, he says they "saddened and shocked" him. "It would even sadden those opposed to the ordination of woman - like John Halliburton. I find such intransigence and fundamentalism very sad."
But he adds: "It was a difficult struggle at the beginning but it is quite different now. Things have changed out of all recognition. It's all water under the bridge. Everyone holds Lucy in very, very high regard. She has won over their respect because of her own innate qualities as a person and a priest."
Rev Winkett's aim, she says, is to forge links with the opposing camps. And over time, she has developed a strong, respectful relationship with her main opponent, Canon Halliburton, who, in turn, has attempted conciliation.
"We could all go into our own corners and dab our brows and feel sorry for ourselves. But that's building walls, not breaking them down," she said.
Dr Moses, however, believes it will take some time and patience to break down the fundamentalist side.
"The vast majority of those opposed to the ministry of women have become more vociferous and entrenched with time," he explains. "It is something we must cope with - and it will not disappear overnight. It is something which will take a generation or two."
But he has one simple, forceful message for the opposition. "There's no turning back now."