If you'd like to play by their own rules you can do this:
-Accept to increase the price and offer 5k in total extra to 'tide them over' until signing.
-Drag out the process as long as you can, tell your solicitors to take their sweet time. Don't directly nag or do anything like that, just instruct solicitor to take 3-4 days for each reply.
-Let them get anxious and very eager to sign. 1 Day before exchange is due, notify them that you will be offering 10k less or you will withdraw.
This is of course will work one of two ways, either they'll be so fed up by then they'll accept or they'll tell you to jog on. Either way you'll have wasted as much of their time as they did yours. And don't worry about the house, there's plenty of stock out there.