I found exactly the same a few months ago. My wife rang the dealers to check availability of vehicles as a private person and told vehicles would be within a 2-3 month period while they transfer stock and prep the vehicles. Then a short while later, I rang as a Motability customer and were told a minimum 9 months more likely 12 months.
When I mentioned this to a Motability, they were adamant it does not happen!
However, speaking to a VAG group sales guy whom has recently retired. The profit on Motability cards is so low and the paperwork so involved, they would now only like to sell to private customers. Many dealers want out of the scheme altogether but fear the bad PR that will come from it.