I still don't get why you'd want to pay them anything, for anything to do with the shed.
It was made clear on the legal papers provided by the vendors and their solicitors (property information form, and fixtures and contents form) that the shed was excluded from the sale, ergo, you are agreeing to buy the house and garden minus shed.
They now want to leave the shed. It is worthless to you and an inconvenience. TBH it is irrelevant how much it cost them, how much they think it's worth, and indeed, what it is. The point is that they are planning to leave a pile of assembled rubble in your garden. Would you be offering to pay to store a load of black bin bags full of rubbish? No, you'd want them cleared at the vendors' expense. Same deal here.
As I said we went through something similar. I told the vendors that the situation (of their making) would be resolved at their cost or we would exchange on the sale of our house and move into rented, walking away from the purchase. Not ideal but with stagnating/falling house prices forecast, we'd be in a much stronger position as no-chain cash purchasers than they would be trying to buy onwards with a fallen-through sale and going back in the market.
Time to toughen up. Either demand they remove it before exchange, insert a retention clause/removal date/lack of liability into the contract, or offer to keep it for a reduction on your offer price and dispose of it yourselves at your convenience (having used it first - if there's access to the garden not through the house, I'd be keeping that shed until all necessary work was done on the house! ).
Remember - you don't want it, they said it wouldn't be there, you are not going to pay for their rubbish.