Update: The best I can do so far
York to Cheltenham Spa offpeak return (SVR) via not london 71.00 restriction 2v valid after 0930, priced by crosscountry
Cheltenham Spa to Teignmouth Off peak return (SVR) via any permitted route 39.70 restriction WG valid after 0825 from Cheltenham spa and 0833 from Teignmouth, Priced by FGW.
Total 110.70
The 70p can be saved by splitting at Taunton...
This saves just under £10 on the through fare, but the through fare is valid at any time from 0500.
To leave earlier:-
York-Sheffield Anytime Rtn £18.80
Sheffield-Birmingham Off Peak Rtn £34.80
Birmingham-Cheltenham Off Peak Rtn £19.40
All totals £73 which is £2 more than York - Cheltenham but then valid on any train to Sheffield, and at or after 0930 from Sheffield.
I'd get Advance fares via London if possible. When AP tickets go on sale you'll get a better deal on EC/FGW than on XC, if changing trains isn't a problem.
Advances are available from 16.00 in theory although the cheapest I can find actually available is 27.50
Yes the cheapest AP fares never seem to be available on XC.