It would probably be better to differentiate it under a title of "Premium Seating" or something similar. You could, in fact, be abundantly clear about the levels of First Class provision by having a national network-wide branding scheme. For example, Premium Seating would offer little more than a guaranteed seat and maybe power sockets or bigger tables. Business Class (like Chiltern's Business Zone) would offer a much-improved seating layout and a segregated area but few if any complementary items. First Class would offer the full monty in terms of free food and drink, dedicated staff and guaranteed free wifi.
Premium Seating would obviously still have its enforcement issues, but perhaps would be treated somewhat differently - acknowledging it is effectively only a paid reservation system, in the way that First Class in the southeast basically already is. I would suggest a "pay for it or leave it" type of attitude to enforcement - with a flat or zonal fare which would only be discounted if you were (say) a Gold Card season ticket holder. It would be hard to know exactly when, if the person responsible for charging the fare couldn't get through the train (eg. due to overcrowding), it would mean that it wouldn't/shouldn't/couldn't be enforced.
Any civilised society should be able to cope with this sort of thing - the deckchairs in some of the big London parks are able to be hired on the same principle. You can rest for a moment or two, but any longer and someone will come up to you and ask you to pay, or explain that you need to go away.
I suggest there would be a multi-purpose area for wheelchair users, luggage and so on - and there would be lockable foldable seats for crew in that area. Something like the arrangement of the wheelchair area on a 387, but a bit smaller, wouldn't go amiss. The seats have fold-down tables available and are relatively comfortable despite being foldable ones.