For a man who is about to help oversee the largest, most expensive and most complex salvage operation in history, Nick Sloane is remarkably sanguine.

Sitting in a seafront bar, exchanging wisecracks with passersby and enthusiastically describing a hog roast he is planning for next week, the 52-year-old South African exudes a geniality which belies the pressure he is under.

Next week, before they can enjoy the roast, he and his colleagues have to try to pull off an exercise which is unprecedented, not only in terms of scale and cost, but also of methodology: the righting of the Costa Concordia.

If all goes according to plan, the stricken 114,000-tonne cruise ship which crashed into rocks off Giglio island in January last year, causing the deaths of 32 people, will be pulled into a vertical position and left to rest on underwater platforms.

This so-called "parbuckling" is a crucial stage in the plan to remove the Concordia from protected Tuscan waters in one piece.

After months of modelling, calculation and planning, Sloane says there is a "90% plus" chance it will work. And if it doesn't? "I have a helicopter on standby," he says, deadpan.

He is joking, of course, but if there are problems with the rotation, nobody will be laughing – not Sloane, not the islanders, not the Italian authorities, and especially not the relatives of the two Concordia passengers, Russel Rebello and Maria Grazia Trecarichi, whose bodies are believed to be still inside the wreck. Their recovery, says Sloane, is one of the priorities of the parbuckling exercise.

Ever since it ran aground under the captaincy of Francesco Schettino on the night of 13 January 2012, the huge, listing, rusting hulk of the cruise ship has loomed over the port of Giglio, the low roar of the salvage operation a permanent feature of the usually cheerful seaside town, and its partially visible white hull a constant reminder of the tragedy that unfolded that night.

Twenty months after the disaster, Schettino is on trial for multiple manslaughter and abandoning ship – charges he denies. The Concordia, meanwhile, still lies, half submerged, a few hundred metres from the shore off Giglio.

As the ship sank in waters famed for their biodiversity, there was never any question of it being broken up on site for fear that this could cause environmental damage. Instead, an ambitious plan by the US company Titan Salvage and Italian marine contractor Micoperi to parbuckle, refloat and eventually tow the vessel in one piece to an Italian port was deemed the best option.

When work started last year those involved realised they faced an even greater challenge than they had previously thought.

"Basically, the more we found out about the ship the more scared we got," says Sloane, senior salvage master for Titan. He says the chief complicating factor was the ship's location, balanced precariously between two spurs of rock on a steep underwater slope. Such is the resulting incline that anyone who goes on board has had to take a climbing course beforehand.

The teams had to act quickly to stop the wreck slipping any further down into the sea, filling the gap between the outcrops with grout bags of cement, and then moving on to the construction of six underwater platforms – the largest of which weighs about 1,000 tonnes – on which the Concordia is expected to rest once upright.

The drilling of those into the granite caused the teams great difficulty, says Sloane. "You imagine drilling a piece of glass at a 45-degree angle with a hand drill: the drill just wants to slide down the whole time. We had to drill all the holes in exactly the right locations so that when the platforms arrived they fitted the holes and there was 1% margin of error," he says.

The biggest challenge, however, is still in store. The head of the Italian civil protection agency, Franco Gabrielli, announced on Wednesday that, after months of preparation, Monday would be the first possible day for the parbuckling to take place.

On Sunday the weather conditions will be checked and the situation evaluated. If the green light is given, Sloane and his colleagues will "pre-tension" the wreck that night – a process involving an initial exertion of force to let it "soak through" the steel and prepare it for what is to come.

At around sunrise the following day, the rotation will begin in earnest, with computer-operated strand jacks being used to tighten cables and pull the ship slowly upwards without, it is hoped, twisting or breaking its main structures. The operation is expected to last between eight and 12 hours. And once it is started, it cannot be stopped.

"All the forces you're putting on her will cause a lot of deformation, so the weaker elements will deform and some will fracture," Sloane says, explaining that this is an expected and not necessarily problematic element of the plan. "And if you put it back again then that's it, you've lost the chance. You only have one chance from the start."

Parbuckling is nothing new; it was used, for example, to right the USS Oklahoma after the battleship was sunk at Pearl Harbour and to salvage the Herald of Free Enterprise ferry after it capsized at Zeebrugge in 1987.

But the sheer scale of the Concordia – a 950ft-long palace with 13 bars, five restaurants and four swimming pools – makes all the difference, as does its internal structure and positioning. "To do it on the side of a mountain like this, with a massive ship … that's what is unprecedented," Sloane says.

The challenges are reflected in the cost. According to Franco Porcellacchia of Costa Cruises, the ship's owner, it is now estimated at €600m (£505m), the most expensive on record.

And the weather – which Sloane describes as the salvage master's "worst enemy" – has not helped, either. Last winter brought Giglio some of its worst weather for 45 years, and the project fell significantly behind schedule, spreading despondency among the team of some 500 workers who, between them, represent 26 nationalities.

Time is now of the essence. The wreck cannot spend another winter in its current state. As clouds pass over the island and a faint chill is felt in the breeze, Sloane notes that the summer is already fading. If on Sunday the conditions are not good enough, they will check again every afternoon until they are.

Once the ship is pulled upright, it is unclear exactly what the next steps will be. The team will have to establish the extent of the damage on the starboard side and then start welding sponsons – huge hollow steel boxes – onto it. There are already a series of them on the parts of the ship that have been above water, and, when the wreck is finally re-floated next year, the sponsons should act as "armbands" for a vessel badly in need of greater buoyancy.

Concerns have been raised in recent days over the potential environmental damage that could arise from the parbuckling, with Italy's environment minister reportedly writing to Gabrielli and asking for the details of contingency plans to cope with any "eventual environmental emergencies" that could result from the process. Last month the environmental organisation Legambiente staged a protest demanding the ship be moved as soon as possible to avoid disaster. But Sloane remains unruffled by such pressure, insisting that the environment has been a priority throughout the plan and that the waters surrounding the wreck are "the most monitored and controlled section of water in the world at the moment".

As for what happens on the day itself, he appears, once again, sanguine. "You have to be patient and just wait. You're never sure what you're going to get until it happens, right?"