OK. If you want to try Gutenprint, don’t use that profile. It will not do the right thing.
The profile needs to be specific to the driver as well as printer, ink, paper, and (usually) resolution. That’s because the ink generation is done in the driver, and different drivers may not generate the same output from the same input.
In the end I managed to succeed with Gutenprint and I’m glad with that. I’m quite lucky that support for Selphy was recently added.
Long story short: The biggest problem was to simply choose Print with Gutenprint instead of using Print entry in menu. I have wasted like 5 dozens of Selphy sheets and lost like two weeks with that. I just couldn’t figure out why after Convert to profile prints look like without this operation. Then just almost accidentally I tried different method and choose Print with Gutenprint and it worked! Well that was trivial…
I print with gimp so that I can convert to profile, rescale, resharpen and so on before print. I prefer gimp so that I can safely rescale image to avoid problem I’m describing below.
Main difference for Selphy between Turboprint and Gutenprint is that photos from Turboprint are a bit blurry and from Gutenprint are sharp. I thought it was nice until I have discovered that there could appear stepping around some shapes with high contrast (white collar, hand in the air). I don’t really know what causes this issue but rescale in gimp to be 300dpi helps a bit.
Of course I have profiled my Selphy with Gutenprint and that gives great results. I tried once a profile done on Adobe Printer Utility and with gutenprint it was way off.
Thank you @rlk for maintaining Gutenprint.
Gutenprint doesn’t interpolate the input; if the input resolution is significantly lower than the printing resolution, there can be stair-stepping.
It was just the opposite. The image’s resolution was significantly higher than needed to print in Selphy (4x6"). Thus maybe it was printer itself?
Nonetheless now I use Gimp for printing and scale images to match the final print.