That is kinda baffling
I'm grasping at straws a bit, but just to ask.
If you remove the spark plugs to make it easier to spin the flywheel (and listen), the coil is never actually touching the flywheel, is it? No high spots on the flywheel? No shiny spots on the coil surface? In your last pic, the coil looks pretty close to the flywheel. I'm not an EE, but perhaps if it touches the flywheel/magnet, it makes the coil not function properly.
Whatever you're using to set the gap (I used a business card), can you keep that between the coil and the flywheel, as you rotate the coil through a full revolution, to make sure the coil is never getting too-close?
If I'm re-reading the thread properly, you've never gotten spark on the troublesome engine, or at least never gotten the engine to run, right? Just want to make sure I've got straight which combinations do what.
The flywheel, and the flywheel magnets, are common on all of this, with the "bad" engine, and the various coils. Can you hold a piece of steel against this flywheel magnet, and see how strong it feels? Then hold the same steel against the flywheel of the good engine? Maybe the magnet is weak somehow.
A crude test that I'll do, when trying to see if the spark is just weak, is to decrease the spark plug's gap significantly. A smaller gap is easier to jump. So if the coil is producing *something* (vs being grounded out, for instance), just not enough to jump the normal plug gap, you might then show a spark. Which would then help better-understand what's going on.