You're welcome.
Yes, I think the overheating was the reason of an erratic behavior. When I got the bike, I soon found out that the PO was running her withour any air filter in the air box and when I resetted the ignition timing, I found out that it was originally wrongly set with too much advance (despite the timing having been done by a professional bike shop less than 300 miles ago, with a carb cleaning...).
My second guess is that they didn't diagnosed/suspected the Eureka system and, like often, confused ignition issues with carb issues, trying to mess around with the carb and air filter to correct the errand revving of the engine.
(NB : that bike shop was run by a RE distributor and a supposedly "RE specialist mechanic..."
)
An I was unhappy from the start to get a bike with an aftermarket Eureka ignition on it. I agree with you that it is a bit of an overkill accessory on such a low revving single cylinder and I prefer my Bullet still "untainted by technology" on this issue. Points are perfect for that kind of engine and their accessibility on the Enfield is just a matter of seconds. Great design.
But the capacitor is a great (and cheap) improvement. You can even kick start the bike without any battery connected. Associated with a good Rec/Reg, you got a "Powerbox" equivalent for a third of the price. And you can even argue that it is not really a technological improvement since capacitors were widely used on all 50's motorcycles.