Also test your coil before trying another CDI. It's an easy test. One multimeter probe in one plug boot, the other probe in the other boot and check resistance. Should be between 3.5 - 4.7 k ohms. I've had two coils flop on that test, switch out and problem solved. I've noticed when the coil starts going funny they tend to intermittently run on both cylinders, sounds kinda like an old Lawnboy on the water lol. If the coil passes that secondary winding test, then try the primary winding test inside the ebox since you might be in there anyway. Orange on one test lead, black on the other, 0.078 - 106 ohms is the spec.
Edit: While I'm thinking about it, I was able to drop in an enhancer while running my oem 38's even though they were set up on an oem CDI, at first start the enhancer revved the motor to the moon but afterward settled down. But, I just setup a pair of SBN 46's on the enhancer according to different specs right off the bench, it ran quite well until the enhancer started triggering backfires. When I first ran the enhancer on the 38's last year at the end of the season after it had it's little runaway fit, the ski would run for about a minute or so, then just shut down like the lanyard was pulled. It did this about a dozen times and for some reason cleared up. This year after getting the new 46's mounted up and set to go, just after getting them tuned with the enhancer still onboard something started causing a backfiring event. As soon as I would touch the start button a hard backfire would happen at the first compression/combustion and stop the engine rotation dead. That seemed to only happen on a cold engine. After it was running and warmed up it would start fine. Let it get cold and same deal, backfire at the first combustion stopping the engine dead. I pulled the enhancer after reading someone else had the exact same problem, swapped with an oem CDI and that was the end of the issues. I did the same, put an oem CDI back in and could not get that engine to run well worth beans. In fact I'm still chasing down the gremlins with suspicions that the enhancer's backfire may have tweaked my flywheel key. I'll know tomorrow but the point is, yes the CDI did make a difference on carb setup. I had those carbs tuned to where the enhancer seemed to like it and would peak that engine out extremely well. Not so for the stock unit though. I couldn't get the engine to run well on those particular carb setup specs. It was lazy and wouldn't get past about 6200 RPM. I had to change my jetting to make that happen. I have also read that the oem 38's are much more forgiving in an all around situation whereas the higher performance carbs like the 46's are a lot more picky about how finely tuned they want to be to run well.