Your profile shows an unusual concentration in the gamut around the darker, semi-saturated colors around the entire color range. If you look at the attached 3D gamut, we usually expect a good gamut volume to have a smooth wireframe representation all the way around. But your profile has some kind of girdle. A closer look shows that the colors are folding back on each other in this area.
The bottom line is that you have a bad profile. This profile will give you these harsh transitions all over the spectrum, not just in the flesh tones. My wild guess is that it’s due to a multi-page target, where one page was printed slightly different from the others? It could also be due to a hiccup in the measuring of the targets. So try measuring your targets again and make a new profile. If that does not improve things, you’ll want to print all new targets, measure and create a new target.
I’ll be a little surprised that this has to do with measuring problems. Modern profiling software and hardware like the i1Pro you’re using are very well established in their procedures these days. It’s pretty hard to make an egregious mistake and get away with it. The software will tell you to read the line over again or something. So even though you’re a newby, it’s pretty unusual for a profile to be made that behaves badly like this.
Here’s a video showing a look around the gamut in ColorThink’s 3D Grapher: