I have printed a fair number of large prints on Canvas. Your results may vary, but my results which are consistent and reproducible are:
1: You mention canvas AND canvas paper by which I assume you mean a paper with a canvas finish. I have printed on both and can categorically state that in both cases a good ICC profile is essential for the exact reason you mention - low DMax and low contrast leading to muddy looking solid areas and three-quarter tones. Generally, the canvas surface will diminish the reproduction of fine detail. With correct subject and careful printmaking, the result can be outstanding.
In my case I printed the paper with a canvas finish using dye inks with good results. I did find a coating increased the black density and brightened the image. - I used Breathing-Color's Timeless Satin.
On the genuine canvas - I printed with pigment ink for the longevity, and again applied a coating - This time using Premier Eco Print Shield - Satin finish. My research indicates this is the same as the Timeless - merely rebadged and cheaper. Results were truly outstanding by my obviously biased opinion. The substrate was Red River Blanco Canvas and Breathing Color Lyve Canvas. Both supply their custom ICC profiles and I could not tell the difference between the two prints. The Red River product was half the price of the Breathing colour, at least when delivered to Canada.
You may find the following information of use. Relates to the effect of coatings on the final image complete with reference data. Mark McCormac is an impeccable source
https://www.dpreview.com/forums/post/59079475
https://www.dpreview.com/forums/post/59079475
2: Your original message also refers to metallic papers. Again the world of advertising muddies the waters, and a large number of differing products could meet the criteria.
My own experience has been pretty extensive with Red River Polar Pearl Metallic. Outstanding results with either Dye or pigment. Slightly better pop and contrast with the dye inks.
Have a few Moab metallic papers to test - but have not got around to them. They are so expensive here in Canada and I am afraid the test may be successful and consequently expensive.
rs