Larry,
Not sure if this will help your situation or not, but I had a similar situation with my 912ul in 2007. It started running really rough when I had the plane at the Seaplane Base at OSH. During the week I had countless friends and every Rotax "Expert" I could find try and help me figure out what was wrong. But after a whole week of messing with it, the problem still persisted.
So after the convention I dug into it, and eventually found the problem. I narrowed it down by looking at my spark plugs, only to find one lower plug that was not burning as clean as the others (it was obviously firing, but was sooted up considerably more than the others). I traced back the wiring to the coils and modules, and finally...I found it!
A wire coming out of one of the igntion modules had a broken wire between the module and the multi wire connector.
On early 912ul's the wires coming out of the ignition modules are so short that the weight of the connector shaking during engine operation fatigues the wires to the point they can break. In my case just one wire was broken which controlled that spark plug. And even worse is that it would occasionally make contact, making the condition very intermittent (and hard to find ). I repaired the wire by braiding the wires back together as good as I could with the short wiring, applying a very light solder job over the braiding, and then sealed it up with heat shrink tubing. I know it is generally viewed as a no-no to use solder on aircraft, but my only other option I could come up with was to buy a big buck ($800??) ignition module. Repairing it solved my problem, but one day I may have to replace that module.
Apparently Rotax is aware of this problem as all the new 912's use longer wires from the box to the connector, which makes it much easier to secure the connectors without fatiguing the wires.
On a last note, I also helped a friend fix a brand new 912S that ran rough right out of the box. Again, he contacted every Rotax expert he could, but nothing helped. So one day we were looking it over together and I noticed that he had moved the wire coming off the stator to one side to give it more clearance. We moved the wire back to where it was originally, and amazingly we fixed the problem. Apparently that wire is very sensitive to where it is located on the back of the engine and/or how the shielding is grounded. This may have been just a fluke since normally we aren't moving stator wire locations on our engines, but it might be worth looking at in the case you have damaged shielding, broken wire, etc.
These are just a couple ideas I had to try and help you out, as I'm sure this is killing you knowing the busy summer flying season is almost here.
Paul Seehafer