Via Northampton is mandatory because of a specific rule around signallers diverting trains that way without prior notice (but will have booked work too).
I'd expect via Coventry and round the back way to Stafford via Stechford and Bescot, avoiding Wolverhampton.
Probably via Hixon/Norton Bridge and then Stoke/Alsager.
And probably one route via Manchester.
With the 222s, they do have the option of travelling via Settle, but I very much doubt it, especially in DOO mode. Perhaps for very long engineering blocks by special arrangement if someone is feeling generous.
If/when Stirling gets Hitachi units, you may well see Newcastle-Carlisle and other positioning moves if the diagrams can be better managed in that way, or if the West Coast is closed and they run a 10 car from King's Cross and split somewhere, like what occasionally happens with combined Hull and Lumo services.