Usually my go to when dealing with something that can be problematic for regular embroidery only, I'll either go with a lattice motif fill underneath and embroider on top of that or applique a piece of fabric and embroider on top of that.
Use the same color as the substrate for either the applique or the lattice motif helps "hide" the extra production techniques to facilitate the embroidery.
Lattice motif is what I tend to do while trying to tame pile on towels (just if that ever comes up for you).
For police vests though, patches would probably be the my first bet in this case. They should be used to having patches on their stuff. If you don't have a merrow machine like a MG3U for the overlock border, just applique twill using a satin border and finish off with your embroidery. For applique border stitches, already use a denser satin stitch, so that will help those satin stitches.