Perhaps an Off Peak Railcard is what's needed? No travel before 09.00 or between 16.00 - 19.00 perhaps? Utilise some of that daytime capacity, might be particularly beneficial for increasing off peak demand on routes where Advances aren't available?
Have you seen the SNCF Jeune Carte? 50 Euros a year for those aged 18-27. On reservation compulsory trains you get 10% of Prems fares (the cheapest, inflexible Advance tickets), 30% off Losisir fares (semi-flexible mid-priced Advance tickets). On non-reservable trains a discount of 25% applies at peak times and 50% at off-peak times. Peak times are shown in white in the attached image and (shock horror) actually correspond to the busiest times of the week for train travel.
I have no wish to upset Yorksrob but the French offer a weekend railcard which anyone is eligible for (Edit: it might actually only be anyone from the EU I'm not sure), although it does cost 75 Euros a year. I wonder if RDG are looking closely at a National Weekend & Bank Holiday card as part of their research?
Translating this into something that might work in the UK is difficult but I think that Monday to Thursday daytimes are a good area to look at offering a greater discount, both by making more people elligible for discounts and maybe also by offering a bigger % discount. If the trade-off is a smaller % discount on Friday evenings and Sunday afternoons then so be it.
[For those unable to see the image time restrictions are generally 2 hours in the morning and 90 minutes in the evening, except Fridays and Sundays where most of the afternoon is barred, and there are no restrictions on Saturdays].
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