Hi Owain. One more try. Get yourself some plugs from a running engine. I re-read this thread and see you have new NGK plugs, which have (I understand) been the subject of counterfeit operations. Maybe you got unlucky.
Give the cylinders a good dose of fresh fuel down the plughole, then maggy end cover off, fuel off and get kicking with no choke, varying the throttle. It should fire and run for a couple of seconds. If successful, repeat with the fuel on and a bit of choke to keep it going.
If it is still dead, time for another go at the magneto. This is still your number one suspect, reviewing this thread again from the start.
If it will only run with continual priming down the plugholes, that suggests the carb is acting up. Try your old carb, cleaned and checked, the new one may be not as good as it could be. Check the fuel lines, just in case some sediment is being drawn down after your heroic test run.
Once running OK cold, the classic symptoms of a failing condenser are a reluctance to start when hot, and erratic running and sudden cutting out, again once hot. The condenser within the magneto is buried in the armature, at the drive end, where it is nice and warm.... they have a hard life.
The Brightspark Magnetos Website will tell you all you need to know about why they fail and the simple effective options for a fix, essentially and very sensibly moving a modern type condenser to the points plate for easy access.
If you go this route the existing armature does not need a rewind, just as long as it is electrically sound, and is used with a slight circuit alteration to isolate the suspect condenser. In the end the choice is yours, but for my money, conversion to an easily access Brightspark condenser makes good sense if you are determined to retain a standard magneto.
For a simple assessment of your magneto, I would recommend Priory Magnetos. Here bear in mind this is a small business, and opening hours and availability of service depend on existing workload, so best to make contact first by email via the website. If the armature turns out to be the problem, electronic ignition, typically Thorspark, is a good choice as it retains the defunct magneto with ATD as a basic mounting and is fairly priced compared to a full house rebuild of your suspect magneto.
Swarfy.