The other train options are-
1. (which would need to be booked as 3 tickets) is-
Edinburgh to Carlisle (Avanti West Coast) d 0852, Carlisle a 1005,
Carlisle to Leeds (Northern- via Settle and Carlisle line d 1058 Leeds a 1338
Leeds d 1351 (and frequent, both Transpennine and Northern) York a 1413
At the moment Northern are 2 weeks off opening bookings for Legs 2 and 3. To be honest I would just book at Leeds for leg 3. But wait for advance bookings for Leg 2, and you should get it for £10.50, rather than full fare of £38.50.
Or 2. Edinburgh to Manchester Pic d 0812, Manchester 1126 , Manchester 1158 York 1336- both on Transpennine (2 tickets)
Or 3. Edinburgh 0812 Preston 1045, Preston 1144 York 1357 on Northern (that is the cheapest route at £12 + £10- to Preston you can book now, Preston to York opens in 2 weeks time.