Colormunki printer profile
It doesn't sound like I can tell you more than you already know. I don't have a Colormunki but I am interested in one. I had an old it8 scanner card and used ArgyllCMS with what I think are good results for that method of profiling. I also have an old puck that I used ArgyllCMS to profile the monitory. Like I said, I think it did very well under the circumstances. FWIW, ArgyllCMS will also use a Colormunki as a measurement tool.
There seems to be a few options here.
1a. A profile is being applied when printing the target. ArgyllCMS recommended I use Adobe Print utility, if I remember right. I would think that the software Colormunki is using would be sure to avoid adding any profiles.
1b. The way you have the color profile applied is incompatible to how the profile was created. I use LR to print, and I have used QImage. Both of those apps will apply the profile used outside of the printer driver. I left the printer driver in the same state for the target printing and the profiled printing.
2. The printer driver is actively adjusting the output. I would say that this one is obvious, but some drivers have multiple settings that modify the output. I was profiling a Brother printer (I was happy with the Epson), and it was a pain to get rid of all color management with that driver. The no color corrections was obvious, but it had a buried option to match the monitor output (profile).
3. The Colormunki isn't calibrated. Don't know what to say on this one other than I would hope that isn't it.
4. I would assume driver issues with the colormunki could also cause problems. But I would think that is a pass fail option. Maybe if the driver is too old compared to the device.