"At least in Windows, the black ink is only selected when you change the Media Type in the Printing Preferences dialog, not by the ICC selected in the program doing the printing."
Correct, the ICC profile it self has nothing to do with changing what type of black ink the printer uses. However the manufacture of the ICC printer profile you are using should tell you what media type to set in the Epson driver which will then choose the proper black ink.
"but that some of the media types will allow you to select manually."
I have used sample packs from most of the popular paper manufactures and none of the profiles I used with any of them let me choose between which ink I can use with a cretin media profile. I had one that said (Breathing Color) I could use one of two different media types like glossy or mat which will then choose the different blacks. I tried this once based on the manufactures suggestion. I used a media type that used photo black on some mat paper and the out come was less then acceptable.