Well, if cutting days off of any of the Scotland days is possible, THEN I'd strongly recommend a Hadrian's Wall stop or two and then York. Keep the car a bit longer and drop in York instead. If you can't do this, then I'd agree that York is best and maybe easiest.

Yes a sweet drive would go or could go from Edinburgh via the Borders Abbeys and then down to Hadrian's Wall - Hexham is a nice regional town to stay in there - and then pop down to York the next day, maybe even going thru the Yorkshire Dales though that can be slow driving on minor roads.