I also don't understand how you can get the inline spark tester to work when the white wire is disconnected from the coil. The only other thing you say that does not seem right is that you connect the white wire back to the negative terminal of the coil. My ski is remote from my home location and I am recalling from memory and looking at the schematic for your ski. The bottom of the coil has 3 connections, the main post and 2 fastons. The main post is case ground (negative) and has a lot of black wires connected on a bolt through it. One of those black wires goes to one faston at the bottom of the coil which is coil negative. The other faston at the bottom of the coil would be where the white wire goes and that would be coil positive (not coil negative as you state above). Is that how yours is wired?
The only other thing I can tell you is what I observed on my ski while diagnosing no spark problems. I never tried to measure the voltage at the CDI while cranking (except when I found out it dropped completely when I determined the holder relay was faulty). I would usually test it connected directly to the battery while cranking if I suspected a marginal battery. I would notice if the voltage dipped to around 10 volts the ski would crank but not fire. A good battery, or even a marginal one freshly off a charger, will not dip that far while cranking.