I put an 13" SBC Con-oFE in my 99 CTD several weeks ago. With the 13" conversion, there's no question, a new flywheel was required. And after pulling the stock clutch out, there was no doubt that the old flywheel was unusable, it was burned and checked. You've already got a 13" clutch in front of that 6spd. I do know a lot of people would just say to run it. Me, I'm a little paranoid, I'd either have the flywheel turned or replaced.
IIRC, the note that came with the clutch kit does refer to having a flywheel turned, and not ground, due to the profile.
Personally, I just love the Con-oFE clutch. The only place I've found it to be "grabby" is backing up hill. Any forward engagement is nice and smooth.