In the photoshop print dialog, I indicate 'photoshop controls colors', and I select the ICC profile for the paper.

That is incorrect (and a fairly common mistake).

The printer/paper profile enables the editing program to render the colors the same as how the printer will print them. That way you can edit them to your liking before they are printed. Ideally, your monitor is also calibrated with a custom profile; which enables it to render colors as accurately as it can.

You should not use the printer profile for anything other than softproofing the image within Photoshop.

1. select custom proof colors (menu View>Proof Setup>Custom)
2. select the printer/paper profile to emulate, rendering intent, and paper color
3. enable softproofing
4. edit the image so it will print as desired.
5. allow printer to manage colors (as long as the image is in a typical/known color space)
6. optional- save the proof setup with a custom name in step 2; save the edited image with a new name as it is only (ideally) suited for printing on that printer/paper.

Edit: Alternatively, you can select Photoshop manages colors enabling "match print colors" (and paper white/gamut). That will cause the little preview window to go into softproof mode using the printer/paper profile; and if you don't like the way any of the colors will render go to step one above.