Calico dates back to 1976, long before the own-root rose craze. I think it was a commercial success in its day, just as Patsy Cline, Silk Hat, and many other currently scarce roses were. They grew beautifully as long as they were grafted onto Dr. Huey or some other rootstock, but the only roses left from those days are the ones that will grow well on their own roots or the ones that are still being grafted, such as Arizona, Rio Samba, Double Delight, Perfect Moment, Peace, etc.
I bought Calico and I'm always looking for Patsy Cline and Silk Hat because I remember how beautiful all three were when I grew them in the 1980s. They were grafted roses then, of course, and judging by my experience with Calico, which produces only two or three blooms a year and never grows beyond 12 inches tall, I probably wouldn't be happy with the two others on their own roots either.
Getting back to J&P, the reason I think Caribbean Breeze is simply a renamed rose is that it has no registration name. There's no reason J&P wouldn't have registered all of the Zary roses they inherited, is there? Shazam was one of the roses Zary was testing just before the company changed hands in 2007, and it was registered as JACjosse and entered in competitions in 2008. It was introduced for sale to the public by J&P in 2011. They probably did the same thing with all of Zary's roses.