More afraid of the frame rusting out than the HG causing serious issues. Check the radiator fluid levels and pull the middle spark plug on each side of the engine to see if they're fluid in there. You can also look at the condition of the headers to see where youre at.
I paid about 4.5k for my...
overcharging batteries are bad for them. Running them to zero is bad for them too. You want something inbetween. throw it on a charger/maintainer every couple of days and don't leave it on full time. when you charge the battery you eat up the overall battery capacity by oxidizing the positive...
It does sound like a speed sensor could be a culprit. Intermittent? maybe you can clean the connection with contact cleaner? eitherway, looking forward to the answer on this one.. good luck!