HOTTT!!! coil

A friend of mine and a FABO member passed away several years ago and periodically I help his widow keep his 67 dart going to take to shows. The car has a 340 with Mopar electronic ignition (distributor and ECU), a round (standard shaped) MSD coil and a 2 connector ballast resistor. This system has been in place for a long time. The car has been sitting for 9 months and she went out to start it up for our club's show this weekend (Mopar Magic in Gig Harbor WA). They started the car up yesterday and it started fine and ran fine for a while, then the ignition cut off. After letting it sit for a few hours, it started right back up again and again died after a few minutes. When checking things they say the coil was firecracker hot and stayed that way for a long time - couldn't touch it a half hour later. The ballast resistor was also hot but it cooled down in 5 minutes.

My guess was a dying ballast resistor and recommended that they try replacing the ballast resistor and the coil since it got so damned hot (with a standard coil). Anybody else have insight into this or suggestions on next steps? I suggested that they replace those things, start the car and have someone keep a hand on the coil to see if it gets hot again.