Never heard of the method you are describing either.
Dye sublimation has no feel to the image as the image gets dyed into the fabric and you can reproduce full color photos and designs, but this method is not suitable for natural fabric or ready-made dark synthetic garments.
You may want to look into
DTG printing and screen printing with discharge or water-based inks - these methods are suitable for dark natural fabrics and don't have a heavy hand you are trying to avoid.