We use the Universal fluorescent primer strategy with M13 sequences as described by Oetting (1995) successfully for years on LI-COR 4300. Attached one of our papers for info.
I read your attached paper. I know your co-author Dr. Dariusz Grzebelus from Polland. We used to work at UW-Madison under Professor Dr. Phil Simon, who is a carrot breeder from USDA. We had a couple carrot papers together. Good to see that. The world is indeed small!