The most important thing the paper choice sets is the ink load. Often a setting to achieve maximum ink load without running or puddling is desirable, thus you see many using watercolor radiant white when printing 3rd party canvases instead of canvas.
The platen gap isn't as critical as the thickness setting. The thickness setting when using a paper other than the specific one in the media type isn't always ideal and should be based on the media specifications as supplied by the manufacturer ... do not depend on the media choice getting it right. for example, WCRW sets the thickness to .3mm but the canvas in the original post is .48mm so that setting should be moved to .5mm. If you see smearing from the head moving, then widening the platen gap may help that.
Technically you should use the same setting as was used to create the profile ... I was surprised to find no mention of this on the hahneumuhle site and they only provide a "generic" handling instructions for profiles which refers to using Epson Premium Luster. Sort of lame ... they should tell you exactly what media type was selected, as well as any other conditions that were changed so you can be perfectly duplicate those. there should be a separate data sheet for each profile. Otherwise the profile is invalid. Hard to believe they used premium luster which is the only media type mentioned in their instructions.
If it were me, I'd try WCRW as the media, .5mm as the thickness, and you may find you need to change the advance to allow for shrinkage but that should be tested, as it varies greatly with different canvases.