How is your timing? The pulse gen should be right at the top if the cam and crank are timed correctly, if you got it turned off to the left or right of center your timing is probably off a bit, could be the cam timing is off, i would check the crank/cam timing, its easy enough for the cam chain to get sloppy and skip if it wasn't maintained. From my experience the cam usually ends up being off clockwise when this happens because the resistance of turning the cam counterclockwise with a loose chain causes the chain to just skip a few links. Then someone comes along and tightens up the chain or replaces it and the tensioner and they don't get it timed right. Also check the springs on the advancer, the magnet that spins on the cam, there is two small springs on the centrifugal weights, they rust and fall apart quite often, or just get weak with age and the advancer won't spring back, this allows the magnet to rotate clockwise without much effort, the result is you have to clock the pulse coil clockwise to match it, this would also account for not wanting to idle because the timing is off with this condition as well.
As for the CDI modules... If you bought one of those knockoff aftermarket ones with the round connector that the original plug will fit you will either find that removing the gray wire which is the reverse wire will restore spark or it just won't work at all, i bought a few of them to test, they didn't work on either a 200ES or on my bench tester, they appeared to be wrong internally for the AC ignition system on these. But its worth pulling the gray wire from the plug, you can unpin the contact and pull it out of the connector if you don't want to cut it and then try it again. The other option is to get a cheaper square connector 5 pin CDI and replace the stock round plug for the square plug and make it compatible with more common CDI modules like you find on the other years. That's what i have always done to them. I documented that here on the forum and the dratv.com website has the wiring info and a cheap CDI that works as well.
My 200ES was fouling plugs as well, no matter how much tuning and carb tweaking i did, even replaced the exhaust.. In the end i put a new CDI module on after changing out the plug and it ran great from then on, the old CDI just wasn't producing a good enough spark for complete combustion. It would break up and stumble on acceleration, and it would pop and fart at full throttle. Replacing the CDI fixed that. But since your pulse coil is off from 12 o-clock i would look into timing and the advancer springs as well to rule that out.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....