Originally Posted by Last Tango
I know it's a long shot, but I've seen corrosion in the wires themselves cause internal breaks in the harness. Probably going over stuff you've already covered but double check the internal ground connections around the engine. Pay particular attention to anything that's mounted on rubber/plastic stand-offs because it will rely on wired grounds and I've had issues with these before.
The OP traced the fault to the CDI, but good post before starting to strip an engine down. Outboard manufacturers should be forced to use tinned woring as a matter of course. Any multimeter set to continuity (audible signal) should be the first port of call.