L82c plugs ought to be fine - they are I think the modern L10 equivalent, along with the NGK mentioned by LJ. With a recon'd mag one would hope the HT pickups and slip ring are clean from the rebuild unless you've got a nasty oil leak which is messing things up at the rear of the cylinders. If the HT leads are new too, and the plug caps, and all are screwed up properly . . . . the prob shouldn't be ignition - and you do have a spark! Assuming the basic ignition timing is OK, it might however be worth having a look at the points gap, as that will sometimes alter with a rebuilt item as it settles down. If it's 12 thou odd (or about .3 mm), and close to the same for both cylinders, as it certainly should be with your mag, then that's OK. Spark will be weaker or disappear if gap is too far out.
Choke slide should be fully pulled up - like many of us I don't even have one fitted, as a tickle is enough even in winter.
Was the engine ticking over well when hot, I wonder?
You could check for air leaks around the carb mounting flange, which isn't all that rare. Some carbs (not sure what one you have) have an O ring in the flange that goes on the head, others don't, but all should have a reasonable gasket and make a good seal. The nuts don't want to be done up too tight either, very particularly with concentrics, as that can cause distortion and leaks - as well as in extreme cases causing the throttle slide to jam open. And thinking of air leaks, does the top screw on the carb slide properly? Pilot air should, as you say, be about a turn and a quarter/half/tad more screwed out on a Monobloc.
Whatever gremlin you've got isn't too serious, that's for sure. If the carb has the right jets and slide, no leaks, and there are good sparks and a well-adjusted mag, it'll just be a question of working through the possibilities until hey presto . . .
And one more thing - tappet clearances? If they're closing up when the engine gets hot . . . . that could certainly cause you some grief. You mention compression being a bit less than you'd expect despite decent pistons and bores . . . perhaps a valve isn't seating as well as it should?