Ancient memories here..Back in the 1960's CDI's appeared and promised a better spark. They did for me running a carbureted auto, but the sooty description you describe seems more like a fuel feed problem to me. I am sure you have checked float buoyancy, needle point and seat, stroke of float (low and cut off) , and jammed needle (from crud) by now? Also main jet diameter, (not drill out). The CD I used was great on start up, blasting away at deposits, but unknown by most at the time the duration of the spark was short and not conducive to power production (not a concern here).
Yes, let us hope the good members of this forum continue with the generosity and patience typically shown .