If you want to post pics of your sheath, it might be easier to offer you advice. If you can contact the person who made the sheath, I would do that as well, especially before removing any material.

For res-c I use blue painters tape (typically one layer) around the edge of the res-c (and the blade for the initial forming) so that the Kydex does not bite too hard on the handle. One way to set the tension on a res-c type knife is to have the Kydex tension point where your index finger goes on the bottom of the handle as opposed to on the sides of the handle (see the picture 1 below). The tension is set not on the sides of knife where the Kydex comes up but where the red arrow is below (see pic 2 how the Kydex bends around to trap the handle). Note, this is one of several ways to accomplish this. Other makers may do it differently.

You mentioned the mouth is flared at the moment. You can re-mold the mouth of your sheath with a hair dryer or better yet a heat gun. If the mouth is screwing up the res-c, try putting a layer of tape around the sides of the res-c, one layer should do. Then heat up the mouth of the sheath, focus the heat to the mouth only, don't heat up any rivets and apply the heat only where you need it. Once the kydex can be formed, use a glove and mold the Kydex with your fingers trying to apply even pressure to both sides of the mouth. Using my method, the tension will be set where the red arrow is in my picture below. Keep pressure held for a couple of minutes then leave the knife for about 10 minutes to cool. Pull the knife out, remove the tape and see if the fit is where you want it. If it's not, then repeat the process, maybe you need 2 layers of tape on the side. I would try not to remove any Kydex unless you have to, because you can't put it back. It's kind of tough to put in to words to explain this without seeing a pic of your sheath, but hopefully others can chime in if I am not being clear. Post a pic and I will see if I can offer any clearer advice.