I'm coming at this topic from the profiling end of things, rather than the printing. We have profiled many fabrics including canvas, linens, polyester, etc. Since this media often does not have the dmax that you expect from finer papers, you tend to expect less from it.
However, we have found that by measuring the profiling target with a polarizing filter, we can draw out a lot of the shadow detail that would otherwise be lost. If you're profiling yourself or having someone else make a profile for your fabric, see if you can use a spectrophotometer that has a polarizing filter.