Plenty of good suggestions and choice, how many months have you got
There are some decisions to make, for all or segments, between the best cycling and visiting the most interesting places, my touring leans towards the former, for the latter I mix folding bike and the train or coach. Andyb1's Easterly route has a lot going for it, plenty of interest, but not as scenic (Or hilly) as up through the Pennines. If visiting cathedrals is your thing, this is worth a look:
https://www.cyclinguk.org/cathedrals-cycle-route-challengeAs with the NCN, those routes are best used as a basis, rather than strictly adhered to.
The Scottish borders, as in South of the Glasgow/Edinburgh line, is an area I know little about, but having done a couple of Audax that passed through, they're on my list and there's centuries of history due to the English/Scottish animosity. The area is scenic in a rolling countryside way rather than the wilderness of the Highlands. IMO the North West of Scotland has the most scenic cycling in the UK, even if you don't jump across to any of the islands, but the things to do off the bike are few and far between. Other parts of Scotland have some equally good bits, there's just some less good bits between them.
Couple of other random thoughts:
if you decide to ride out of London, the NCN route along the Lee Valley, from the Olympic Park in Stratford (Not Avon), is easy riding, mostly traffic free, and gets you well clear of the metropolis.
I use trains quite a lot, mostly with a bike, it's a mixed bag, some considerably better than others. I've never failed to get where I'm going, but it isn't always stress free! If taking a London train from Edinburgh be sure to book one that originates there, that's most but not all. it just gives you more time to load and you know the bike space won't already be full. Another vote for booking with trainline, it's one of the few online options where you can reserve a bike space.
I'd second B cereus's point about trying to cram too much in, it's a trap I sometimes fall into, but exploring somewhere rather than passing through on a strict timetable usually, for me, results in more memorable tours.
If the Audax route you originally posted is more your thing, then have a search on RWGPS, for the LEL (London-Edinburgh-London) route.
