B&W prints with Grey Gamma 2.2 profile (DT, GIMP)

Hi,
I have started printing my photos at printing house (Canon iPF 8400 and lot of various papers).
I can manage color printing with provided ICC profiles however I’m puzzled with the B&W option. I should send images converted to the Grey Gamma 2.2 profile for B&W. Canon iPF 8400 has four grey pigments - MBK, BK, GREY, PGY and I’m tempted to try.
There is no straightforward option ‘Grey Gamma 2.2’ in Gimp and Darktable and it seems that Grey Gamma 2.2 is Photoshop’s profile.
The only hint I found is that Adobe RGB has gamma 2.2 and should be OK… and maybe that I could use QTR grey-lab profile.

Any suggestion how should I prepare images in Darktable and Gimp for such requirement?
Thanks,
maciej