It wasn't coughing or picking up at all. I swapped the ignition capacitors out for some higher quality Rubycon units and checked for continuity this weekend and, finding all to be good, threw the CDI back on and tried again. Right as the battery was dying out it caught and fired up and, not giving up the opportunity, I went out for a nice hour long ride. The next day I got it running with just a bit of starting fluid and choke.
I was thinking it might be the signal generator just because it has such a hard time starting up but no issues when running, when the signal generator will be generating the largest pulse. I was also worried about the signal generator alignment as the bike was knocked over a couple times while sitting in the street over the winter.
I'm taking her in to the local shop to check out the cable, as both the cable and housing are busted. If they don't have anything on hand I'll just order a new cable in.