You want to use a relatively smooth canvas for gloss. If the peaks and valleys of the weave are too steep, you get objectionable highlight reflections from the rounded edges of the deep weave. Fredrix 777 has a very fine weave, but very limited gamut and lots of OBA's. Can't get a non-orange red out of it. Currently Sunset Select has a pretty steep weave which makes it not the best choice for gloss, but some recent samples were much smoother. But disregarding weave and OBA issues, Sunset Select shows an awesome amount of gamut and excellent color when profiled from super-clear gloss targets. Very few canvases can cover reds, violets and blues better than glossy Sunset Select.
Canson Museum Art is a pretty good gloss candidate, only 15 mils thick and very smooth with a non-directional texture. You need to build super-gloss profiles to bring the OBA-free emulsion up to truly impressive gamut proportions, it's has a pretty poor gamut when profiled from uncoated targets. Very consistent surface, Canson has excellent QC in regards to surface and weave, and everything else for that matter.
If BC would bring out a smooth canvas with their Lyve coating, it would be great stuff. But the current Lyve weave is too coarse for high gloss, you get terrible reflections when viewing glossy Lyve prints off center when the dominant texture is vertical, and when a print is hung on the wall with the dominant weave texture oriented left-right overhead lighting will haze it out. Bottom line...glossy needs smooth, which is why the so-called Epson Natural Gloss with its deep, coarse weave is so pointless.
The enemy of glossy canvas is of course the "hey Mom! I'm printed on CANVAS!" attitude of most canvas manufacturers. I like canvas not because is looks "like oil paintings" or some such nonsense, but because is easy to handle in large sizes, and because it allows the creation of very large pieces that don't weight a ton. Basically, the same reasons painters like it. So can we please minimize the weave, it's OK, really!