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Then there are the cheap, shiny black and aluminium-effect plastics scattered about inside, more US Ford econocar than true thoroughbred in quality.

Another special extra for the GTX1 is a set of, again retro-influenced, Sparco bucket seats, complete with hard-edged ventilation holes that make them as pleasant to sit on as a case of piles.

Thankfully, the GTX1's glamorous external view is receiving all the stares, even through the bleary, mostly intoxicated nocturnal vision of passers-by.

Even with its roof left in place, the GT40-inspired GT continues to be a car that's more than capable of dropping jaws and opening up wallets of the rich. "The sticker price here is $149,500 [c.£84,600], but I've yet to see one change hands for less than $175,000," says Ewing.

The cost of creating this particular GTX1, meanwhile, can't be easily measured, but it will soon become possible to order something close.

The Genaddi Design Group of Green Bay, Wisconsin, which assisted with the construction of the car we're in and now owns it, is planning to offer a similar, officially sanctioned roof conversion for £22,000.

Tempted by the keys to a Lamborghini Gallardo Spyder, the GTX1's creator briefly bales out. I'm joined now by our fixer for this monumental trip, Johnny Tapanes. We set out on a mission to create maximum impact along Ocean Drive, blatantly ignoring the 'Noise Prevention Area' signs in the process.

Open-mouthed gawps again arrive, and more than most from a man jogging by the edge of the beach, accompanied by his personal trainer. Somehow, he seems familiar.

"Hey," shouts Tapanes. "This guy wants your autograph for his wife!" It's Pharrell Williams, hip-hop, R&B and alternative-rock recording artist, hit-making super producer and widely acknowledged coolest man on the planet.

As I attempt to curl up in embarrassment and hide in the footwell, Pharrell strides over, sweat dripping in great torrents over the dead-pan expression worn on his face. Pleasantries (and even an autograph) are exchanged.

He's been compelled to approach a pair of total strangers by the sight of a car so exclusive, even a man with his level of disposable wealth wouldn't have been able to own it, at least until now. For the GTX1, that's a case of job done.

As Pharrell jogs back off into the night, Tapanes is close to speechless. "You know that guy is an A-list celebrity, and he came over to speak to us," he says. "That just never happens."

Peter Grunert