I have had better luck with mouth calls than cd's. Part of it may be that everyone else around here uses them. Or maybe I'm just good!
The red lens isn't so much a problem as the size of the light, but the red helps. Blue and amber lenses also work well. A lot of people make the mistake of using a huge spotlight when calling. Most coyotes, especially if they have ever been hunted, spook when night turns into day. All the light needs to do is pick up the eye shine. I like a light that is relatively low powered, like a mag-light flashlite. I look around with it until I see something, then I try to call it in closer. When I am ready to take the shot, I turn on the big light without a colored lens. I then have a chance, albeit a short one, to make a positive identification and take the shot. It takes them a second or two to figure out they have been had.
I don't think calling around the dead coons will hurt, but I'm not sure. When I hunt around dead cattle, I don't call, but there is a lot of size difference. The coyotes will find the dead cow one night, but will have to come back a couple nights to finish.