Reading all this has highlighted so many of the flaws and incongruities of the moden, essentially unregulated, insurance industry.
It seems that one consequence of the market's obsession with "the lowest possible cost" is that the service providers seek to mitigate their costs and pass them on to anybody. It is fine if you fit the majority model, but not otherwise.
The insurance industry is heavily regulated but if you want actual satisfaction you will have to work for it as capitalism, inertia and stupidity rule!
The final arbiter is the Courts, but for policyholders you will likely get more (and cheaper) satisfaction from the Insurance Ombudsman. JohnV6 needs to keep both his and the 3rd party insurer on point and get the car repaired to his complete satisfaction. (Motor insurance in the UK is loss-making, so all of the companies squeeze repair/client costs as hard as possible. Current government fiscal policies mean that making a margin on the cash balances is impossible, which used to be where their profit came from).
Remind the third party insurer that you always have the ability to sue the 3rd party for your full costs to restitution. It's messy and slow but they are on the hook. The test in Court is always 'is it reasonable" and "did you mitigate your costs, where you were able"; for a specialist car a specialist repairer is usually reasonable. I would trade a posh hire car for the repairer of my choice.