I have been printing on Jacquard fabrics coated for inkjet usage for about 7 years with pigments, both Epson and carbon monochrome inksets. Some output much better than others.http://www.inkjetfabrics.com/
These days with Ultrachrome, HP, and Canon pigment inks the outcome can be spectacular. Use the Fabrign line of Jacquard fabric, which doesn't require steaming.
The ones I use the most are Japanese Haboti 16mm thickness, for a smooth durable surface and Indian Dupion, for an outstanding textured weave. Seal edges with frey check to avoid freying. The third one is use a lot is Belgian Linen. All of these are outstanding with Cones monochrome pigments for monochrome, which I use on them out of Studio Print. I spray the textured ones with a uv spray like Premiere Art, and even the Haboti to avoid atmospheric contamination and prolong the life of the work. The linen has the best gamut followed by the Haboti and Dupion which of all the silks I've tried are the most vibrant. None will give you the look of a good canvas, though the linen is close, but that isn't the point in using this kind of media in my opion. To me synthetic silks, like polyester are horrible and look like cheap advertising display.
If you are printing out of Photoshop simply add about 20% to your ink limits in the Epson driver for Jacqurd silks, or whatever printer and driver you are using when profiling. This makes a huge difference in imporving both dmax as well as color gamut. They will accept a lot more ink than canvas or photomedia. Studio Print, which is a standard in the fabric industry has the most control over ink limits that I have tried, but is not necessary for great work.
If one is looking for a more transparent media, the Haboti 5mm is fantastic, and has a ghostly appearance, especially when backlit. We often use it in a layered, sculptural context. It even shimmers more, adding to the illusion. A cotton gause they make is very thin and transparent and I've used it with an acetate mirror behind it or, layered, for a totally unique illusionary effect. This is what I love about alternative media like this, it has a physical presence.
Jacquard will sell you a "sample roll" which is 42"x6' to experiment with and profile for about $25.00. Definately do that before laying down cash for a large 42" roll which averages over $300.00. They will also send you a large swatch book assortment of samples of everything they have available which is extensive. However you need to actually print something on these to see what they will do for you.
I am interested in reading the outcome of your search for the right fabric. I have a similar need with some backlit wall hangings that I will print on a Z3100. I have received a bunch of samples from Jacuard Inkjet Fabric Systems, HP and Parrot Digigraphics. I still haven't made selection and order as yet.