With some printing techniques, it can be difficult to achieve the results you want with thickened dyes ~ nevertheless, I give it a go periodically. Most definitely, deconstructed screen printing is chief among the techinques that work beautifully with thickened dyes, in fact you wouldn't want to use textile paint on the screens unless you washed it out right away so the screen wouldn't become irrevocably damaged. Also, direct printing works really well with thickened dyes, and I do it all the time.
These photos are of my last go-round of monoprinting with thickened dyes, and truth be told, I did a bit of direct printing on top of each piece because the original prints weren't what I wanted. Monoprinting, for those who might not know, is where you put paint or ink on a surface -- tempered glass or acrylic work well -- then texturize the paint or finger paint in it, or do something to create an image, then lay a piece of fabric or paper over the surface and roll over it with a brayer or rolling pin. Then pull up the fabric or paper and there's your print.
This doesn't work so well with thickened dye, in my experience. Perhaps it's a matter of getting even more dye powder in the paste than I usually use, but I think it's because the viscosity of thickened dye is just different than it is with paint. Also, I think it might be inherently different because paint lays on the surface of the fabric whereas dye changes the molecular structure of the fiber, so essentially the dye print is absorbed into the fabric rather than staying on the surface as a paint print will.
Since I'm not "in the mood" these days to invest in textile paints, I think I'll stick to what I know works with thickened dyes ~ deconstructed and direct printing!