Softproofing for SaalDigital_SoftProof_Fuji.icc
For sRGB:
It seems to work… are you sure you don’t have both buttons on?
I have not read all the thread but I think the gamut comes from the histogram profile and AP recommended AdobeRGB for printing and sRGB for the web so maybe try that …
Marco this is a good video albeit in Affinity to help perhaps with your situation…I think you will need some adjustments to print…Perceptual Rendering is the best for printing and to ensure you are getting that in DT you should turn on littlecms in the preferences. Next I think but on this I would have to look back but recently AP did suggest to use Adobe rgb for Gamut checking for printing…finally Robyn works through some changes to get saturation etc in check to align with gamut and allow you to print…again this is an example in Affinity Photo but it is a nice work though of the process and reflects your issue here…https://www.youtube.com/watch?v=Lb8_yxRK7gA
Keep in mind that you will first export this image as sRGB or Adobe RGB JPG most likely. Thus keep gamut for those at bay. Then in other program you may proceed.
Directly in dt you must match both, output profile and then later print profile which is quite hard to achieve.
As far as I remember I have Saal profiles for Fine Art in dt (HM papers) and they work fine. Did not try for Fuji. At least for Fine Art Saal recommends using Relative colorimetric in soft proofing. Check it for Fuji prints.
I would first fit this image for sRGB (or Adobe RGB) and then check in GIMP.
… and my personal experience in Saal is that I tried, failed and will not come back. But that was on Fine Art prints.
@maf Looks like no matter what you do or read you will only know by experimenting a bit 
Choosing a Rendering Intent for Your Inkjet Print.
Saal Digital accepts sRGB (all products) or AdobeRGB (for most products) only. I have used their Fuji color profile for softproofing, and it works fairly well. You can refer to How to manage images for web and print efficiently? for a discussion - I stopped trying to convince Aurelien about the usefulness of softproofing and the profiles which I used (Saal Digital’s profiles for large calendar prints), which doesn’t mean I’m not convinced about what I wrote. So I do soft-proofing with the printer profile, but gamut checking with the output profile - only checking for color issues visually. But then I rarely have such difficult subjects as the kingfisher, color-wise.