You can make a sacrificial table/fence and attach it to the miter saw. Adjust the depth of cut on the saw. A piece of masking tape can be used to put a leash on the small pieces, leave the saw down at the end of a cut until it stops. The table/fence in the picture is used up and will be thrown away. An advantage to these is that you know right where the blade will cut and there is no gap in the fence for pieces to disappear through. It will also provide a zero clearance backer until it's a bit used up and eliminate raising hair on the underside and back edge of moldings.