The latest Esk Valley Railway newsletter - see link below - suggest that the extra train will give an arrival into Middlesbrough before 0800. This would mean an outward trip at 0450 ex Middlesbrough.
Strangely, they (the EVR) seem surprised at this early arrival time and consider it to be unsuitable. Have they not looked into it before? You can cross the school train at three locations: Nunthorpe, giving an 0731 arrival into Middlesbrough; Battersby, giving an 0756 arrival (and one train will have to be first in/last out with a long turn reversal time); or Glaisdale, giving an 0909 arrival.
There really is no alternative without signalling & track works.
http://www.eskvalleyrailway.co.uk/newsletter.html
Looking at the 1983 summer timetable, it was possible to achieve a near hourly service for part of the day, but that was with proper signal boxes. Introduction of
No Signalman Token Remote, where the driver leaves the train to exchange tokens in a machine sat in a cabinet on the platform adds three minutes each time.
You can get close to an hourly frequency today but it would be tight and therefore probably not a good idea from a reliability perspective. Also you now have the NYMR services which use up capacity Grosmont to Whitby.