Not sure this would work, but:- go to the website leasing.com and click on the orange coloured box ‘find my lease deal’. then, scroll down to just-above the car images, and move the slider from All to ‘in stock only’. There will be the in-stock vehicles – as built, and with the (any) options as fitted. From there, the leasing company is shown, and can be contacted; so as to find the location of the car. Bear in mind that unlike a PCH deal, the Motability contract has to be signed in person at the dealers location – twice. (Once to place the order, then to enter the PIN to accept the vehicle upon collection.)
I may have misunderstood your post (apologies if I have), but if a car is available through a different leasing company it is not available to Motability customers, as our cars are sourced through Motability Operations which is a leasing company in its own right and buys cars direct, not from other leasing companies. It is occasionally possible for cars that are in stock at dealers to be assigned to Motability customers, but dealers are increasingly reluctant to do that in the current climate as they can usually sell them to private customers at a greater profit.
Also, Motability customers only sign one contract and that is with Motability Operations through entering the PIN at the point of accepting the car. A dealer may ask a Motability customer to sign an order form at the point of placing the order, but that is a statement of intent and not a legally binding contract. As mentioned in another thread, orders can be cancelled without liability prior to taking delivery. Many contributors to this forum have done so over the years.