I did a semi trapunto applique thing recently. I cut the shape from my fabric, then cut the batting just a smidge smaller (not even a full 1/4" smaller), used Elmer's Glue Stick to stick the fabric to the batting, then to stick the batting to the top (where I was appliqueing it), stitched it on with a regular straight stitch, and then went around it with a tight zig zag (like a satin stitch, but my machine doesn't have that, so I do a super tight zig zag instead). You could adapt this to Margo's way of wrapping the fabric around/tucked under the batting as well.
I used a batting with I think it is called scrim on one side so it was more firm/sturdy than regular normal batting.