I can't help you with patches but I have cut a cross in a manila file folder, taped it to the side of my 1st aid kit, and applied a very light coating of red spray paint. The red cross is copyrighted and I have heard that using it has caused some to receive lawyer letters, but using green spray paint is cool. Stenciling is easier than you might think, although it does take a little practice.
I well understand what you mean about coming across accidents. It used to happen to me on a regular basis. I even experienced 1 guy blowing himself up in front of me. All I could do was look at his skinless body and then look at my own pathetically inadequate 1st aid kit. All I could do was talk to him, keep him calm, & get his name and a phone number to notify his mother of what had happened. Thank God the ambulance arrived when it did. He died 24 hrs & 70+gals/fluids later.