Time differences so a bit of a delay to my response. I have read the discussion so far and my recommendation is to build a Tele.
Why because a Tele is a stable reliable base and straightforward. And because you want versatility and stability here is what I would recommend.
So Tele - fixed flat mount bridge for better adjustment with different radii of necks.
(TOM/STP I should have mentioned before are generally a fixed 12" radius that you can adjust up and down for height but not the individual saddles which often come without notches for the strings. So not much use with a 10-16" compound radii neck)
Pickups for lots of versatility perhaps a pair of P-Rails from Seymour Duncan or at least one as a neck pickup. They can act as Humbuckers, P90s or single coils. You can even add a Strat type middle pickup, e.g Brent Mason has a Tele bridge pickup, hot strat middle and a mini humbucker in the neck of a Tele and used it on lots of sessions.
A note on necks. Have a look here. https://warmoth.com/guitar-body-neck-pockets and note that the shape of a tele neck pocket and heel are different to a Strats. But you could put a Strat type neck into a Tele neck pocket but not the other way around.
Here is a Tele build I did a while ago which you might find a useful read.
Natural Ash Tele
Lets keep this thread going and we can zero in on a spec for a Tele and a set of parts if that works for you. I honestly think you might not need much else if the Tele is made versatile enough.
I didn't realize you are in the UK. I like the UK a lot. Wish I was there now! Earlier this year I bought a coffee roaster from a guy who makes them "by hand" from Killgarth, UK. A Cormorant. Lots of great artisans in the UK.
Anyway, as to your email, it is very helpful, and as you say, good to keep the discussion going. It helps a lot.
Here are my current thoughts based on what you and others have suggested:
(1) Telecaster Body (not Thinline) in Swamp Ash with no lam top. For now I am thinking that skipping the finishing myself is a better option. So I am thinking of having Warmoth finish it in Clear., Satin
(2) Top Rout - Neck - Humbucker, Middle - Strat (Single Coil), Bridge - Humbucker. Correct me if I am wrong but I think that routing for Humbucker would work with the SD P-Rails? If not, do I need to rout for P-90?
(3) 7/8" (22mm) Side Jack Hole
(4) Hardtail - Narrow Strat® Flat Mount. Note: Not sure on this one, I am looking for something like what you used on your 2014 build based on your suggestions. Something like the Gotoh Humbucker Tele Bridge maybe? If you have another suggestion, let me know.
(5) No binding, no special body contours
(6) Square Side Jack Plate. Not sure if I also need the Electrosocket Jack?
(7) Schaller S-Locks
For the pickups, I was leaning towards Fralin again, and having them pre-wire the control plate, but am completely open to the SD. I went through the entire SD soldering course a while back and am OK with doing the wiring myself. So, if SD, which P-Rails's are you suggesting? The P-Rails or the P-Rails Triple Shot Set? For the middle pickup I can look around a bit on that and get if from SD or elsewhere. Does going with HSH greatly complicate the wiring? Do I then need a 5 blade switch?
For the neck I will likely use Hipshot again. They are working great on my Strat.
I don't want to use a pickguard but I guess if I decide to I can order one like on your 2014 build if it is cut for a Neck humbucker.
I think this covers things for now. Any thoughts, etc. you or others might have are appreciated.
On an unrelated note, I looked at your thread on installing locking strap locks and I will follow that logic this time. You will be "happy' to know that I have adjusted to my horn strap button being off center and have learned to "love it' and lie with it without any anxiety.