Rather than force everything into pidgeon holes, a better approach, if you want regional differentiation is to only have regional differentiation in areas that have strong ideas of regional identity.
So we have a strong "GBRail" brand, which notionally covers all services except those areas which have a strong alternative branding.
So for example a "YorkshireRail" brand, which would be based on the GBRail brand but with 'Yorkshire' accents in form of coloured highlights etc.
This would allow a non strongly branded unit to deputise for a local branded one without being too jarring, but also allow most services in local brand areas to be local branded without trying to force local brands to cover the entire network.
This I agree with. Most of the current regions, and for that matter thinks like Network SouthEast are fairly artificial, and are not based on places that people are proud to belong to, so contribute little to marketing.
As the double arrow is well known, I would stick with a (perhaps modernised) version of this, with a strong main brand (National Rail is the best suggestion I've seen so far) for all services, other than Wales and Scotland, which do have sensible reasons for their own regional identities. I think a separate National Rail Intercity sub-brand would make sense, as the marketing for these services would be very different than for commuter services, but I would use this for all long distance services, including TPE, Cardiff-Portsmouth, Stansted Express etc that weren't part of the Intercity sector, as well as long distance services in Scotland and Wales. I wouldn't try to restrict these services to just long distance passengers, this would just be a marketing brand aimed at long-distance journeys, so there would be no problem with Intercity branded trains running the stopping services at the ends of their journeys. This could also allow price differentiation on certain routes, such as Gatwick Express and HS1, where tickets could be routed "Not Intercity" at a lower price, but in general Intercity would not be more expensive.
The other local brands would be both for things like National Rail - MerseyRail - based on the same scheme, but with a yellow colour pallette for example, similar to the Stagecoach bus liveries worked before the latest 'improvements', but also for things as small as local branch lines with a tourist focus - National Rail to St Ives - perhaps using pictorial wraps like Wessex trains used to do.
That leaves London. TFL is such a strong brand, and the advantages of integrating with it are huge, so you could put all of the Overground trains, as well as the SW, Southern and SE metros into a white blue and orange livery, it would emphasise that they are part of the london integrated transport network, but you wouldn't want to exclude them from the main national brand, so I would create the main livery such that the two can integrate nicely