The £6.25 fare isn't an Off-Peak fare - it's an Advance. As such, it's entirely down to XC's discretion whether they offer any of these fares. However, any suggestion of profiteering is ill-founded, as (like all the other DfT TOCs) XC don't keep the revenue - they simply pass it on to the DfT.
£17.55 is the cost of the Off-Peak Single, but for only 40p more you can get the Off-Peak Return, the return portion of which is valid for a month. If your partner is making a day trip, buying a combination of tickets is likely to be cheaper, depending on the exact time they're travelling.
As 31 May is an ASLEF strike day, there will be no XC services on any of their routes. As such, whilst you can buy a ticket now, there won't be any trains to use it on and you'd then have to argue with XC about them paying for alternative transport.
There will be services on 1 June, but they may be reduced slightly due to the ASLEF strike the previous day and RMT strike the next day. Either way, XC won't open up Advance availability again until the revised timetable for that date has been published, which tends to happen around a week beforehand.