So one step sideways ... I called up GWR▸ (Great Western Railway) ticket sales and they first told me that I should cancel my ticket. And then after we talked about how losing the 'free' days would possibly end up costing me more, they said I need to go to the local station to work it out!
I'm not sure why the station and the telesales team would not have access to the same computers, but anyway... Next stop Reading Station after the rush hour ends.