You could very well be right about the coil breaking down. This symptom sounds like that COULD be happening. Although the coil and plug wires are sold as a "unit", I believe you can unscrew the cap ( I don't know YOUR specific engine) on the end of the wires at the coil towers and look at the ends of the wires and inside the towers. It's a good idea to make sure the caps are on tight at any rate. One thing I've noticed when I find a coil that is going south (only twice in 7 or 8 years) is that there will be what looks like rust staining on the ends of the wires and inside the towers where the electrical contact is made.
However, I wanted to tell you that we have seen a similar complaint on a small twin recently that ended up being a poor connection at the CDI connector. The guy found it by getting it to act up and then wiggling the connector and having the problem go away. I think he too, at first...cleaned the carb and replaced the jet set..... purchased a coil.....then a new CDI....and...when it still did the same thing, he found that he could actually make the problem happen by pushing on the connector in a certain direction. He ended up doing a bit of McGYVERING to make the connection there a solid one and reported back his success.
I'm hoping you too may be able to do some "wiggle" testing with the ignition wiring and find something going on that can be easily and cheaply resolved. Also, racerone's timing light test is a good one too. I use that a lot myself to identify no spark conditions although, I realize many guys just aren't set up to do that. If your engine is a pull start only, it not only requires that you own a timing light but you must also rig up a 12 volt battery to power it.
QUESTION: have you tried squeezing the primer bulb when the "breakup" is happening? If the problem stops when you do that...it's probably a fuel delivery issue and not an ignition problem at all.
Good luck and let us know what, if anything, you find.