Are you tapering the pleats at the top re: waist?
The front of the apron should be at least 20" at the waist if not 21" and the back should be 19" with the pleats. Given you are working with 18 pleats The pleat taper in the back should be about 1 inch and 1.22" the width of the pleat at the hip. What is the length of your kilt? If you are sewing down the pleats 6" is the length 18"? you need to stitch it down about a 3rd of the overall length.
Sometimes if you prewash the fabric before you start you will have an easier time constructing the garment. It will soften up with time.
Are you top stitching the edge of the pleat?
Did you kick out the bottom of the over apron on the left side, to prevent curl? this would make the bottom of the apron about 23.5" with a double pleat depth.
Anyway check your instructions again and math, work it out on paper with a line drawing and you will get the picture.
Cheers
Robert