@47286Dan your ticket is an Off-Peak Return routed "not via London"; therefore, it is not tied to any specific train or operator; the restriction is merely that you cannot travel via London Terminals. That means you can either travel via Reading and Birmingham - there are other operators' services which would allow you to do this, but it would involve so many changes that I doubt it's realistic.
Alternatively you could travel on SWR services to Salisbury and then GWR to Bristol, from where there are a handful of XC services to take you to Sheffield. But again, not an ideal journey and I would expect the handful of XC services that are running to be very overcrowded (especially on the sections like Cheltenham-Derby where they're the only operator).
Obviously with XC being on strike that would require you to make multiple changes to avoid London, which you will likely want to avoid. Hence
@Mcr Warrior 's advice seems the best way forward to me.
Could a paper Super Off Peak Single (Route✠ANY PERMITTED) be purchased at Eastleigh? Cost = £82.50. Then claim a refund for the unused half of the Off Peak Return (Route NOT VIA LONDON) which should generate a refund of some £88.60. Gets you back to Doncaster via London Waterloo / Kings Cross, works the barriers on the LU transfer, and gives a net "saving" of £6.10.
Yep, in practical terms that is by far the easiest option. It's important for the OP to make clear to Trainline that they're seeking a refund on the return portion of their ticket due to disruption, to avoid the refund incurring an admin fee and being calculated based on the cost of the Off-Peak Single (as this would result in barely anything being refunded).