I think that a Prescot to Leeds CDR, route not Preston / Liverpool should be valid by changing at Edge Hill - and hence from West Allerton.
That would be £21.50 + £10.70 for Leeds - York.
Hmmm. By my reckoning, Prescot to Garforth £21.50 is valid on maps ML and TP which permits prescot-edge hill-liverpool south parkway-warrington-manchester-huddersfield-leeds-garforth HOWEVER east coast doesn't produce this fare when specifying via Edge Hill.
Anyway, that ticket, then another ticket (cheaper than £10.70 or £11.80) for Garforth to York - details sent to the OP by PM.
The first train you could get (allowing for the journey from Prescot you won't do) is 10:06 at West Allerton / 10:09 at Liverpool South Parkway. Between Leeds and York, you need to be on the one train an hour that stops at garforth which is xx57 from Man Pic and xx57 (the next hour) from Leeds.
Can change at your choice of Man pic, huddersfield or Leeds. Will be same platform (plat 8) at hud where there is a nice buffet.