You'll struggle to get a sensible price from any of the big name couriers as they base their costs on a combination of actual weight, total volume & handling criteria such as "Will it go on a conveyer?, Can it be stacked?, etc, etc. The volume is the total dimensions, L x W X H, meaning you will pay for the empty space above the seat base, even though it will be used to stack other freight on, which brings me on to the next problem, the likelyhood of damage for an abnormal load like this is is fairly high. I spent many years working in the courier industry and I can wholeheartedly recommend finding a mate with a van who will take it one direction and not via a central distribution hub where it will get (mis)handled again & again. As the other members suggest, there will be someone travelling in the right direction, even if it means a bit of travelling to meet them en-route.
I know the people that run Interparcel, I used to work with them before they set up the business and very nearly got involved myself. They act as an agent, reselling services for the big couriers, UPS, TNT, DHL, Etc, so may not be best suited for a shipment like this, but probably worth a call as they will be more flexible than the big names & will probably have a lot of local couriers on their books