I bought a car in a very similar way as a project and to be honest applying for the V5 etc was very straightforward, came through as normal with no questions from DVLA. I did immediately SORN it though as it is possible the moment you transfer the car to your name you could get stung with a fine....
My car had been left with an Alfa specialist for some work, this work spiraled a bit in an attempt to get an MoT and the person simply couldn't afford the bill relative to the car's worth (then). Both drew stumps and it was left for a couple of years with the specialist until I turned up trying to buy the integrale in his yard that was in a similar state (I failed in my efforts and got the Alfa).
I did however get copies of the email trail from the owner giving their written consent to the transfer of the car so as far as I am concerned it is a legal transfer. They had moved to the West Country and basically just wanted shot of the debt and responsibility. Got my solicitor Brother in Law to give it the once over legally and after the green light passed over the money.
I'm sure Solo would be more than happy to do the same and provide the owner's email address at the least, the only sticking point would be whether the owner will play ball knowing the Vinci's potential worth. That said though I'm sure Solo's storage fees on top of the welding costs would make it prohibitive for the owner to do much else.
Just my thoughts though and I'd be sorely tempted with this car if I needed another project to work on.