David - what printer, what canvas and where did the profile for the canvas come from? While most inkjet printers will print anything below about 10 RGB as black with no detail, matte canvas sometimes pushes that up to around 15 or so, but it really depends on the printer, media and profile. What are the RGB values that are clipping on your print?
Also, are you printing from LR or Ps and if Ps, what version, and what OS version? If you're on a Mac you could be hitting the wonderful dark print bug as well.
I've been printing for the last week on Epson Exhibition Matte canvas with profiles I made for that on a 9900 Epson, and on an image testing the profile, I can see a tonal jump going up from 10,10,10 RGB but everything below that is crushed. You may need to move your RGB black point into the 15-20 range in order to maintain the detail you're looking for. And if your blacks have a lot of dark color in them, that will only exacerbate the problem. You'll have to both lighten and desaturate in order to address the issue.