Pre-cut the lines with a #11 blade and saw just to the scrap side of that line.

Sandwich the part (pattern on the top piece with scrap clamped top and bottom and keep the middle piece - this is wasteful but works).

Use a finer blade.

Your coping saw should cut only on the push stroke. Don't "saw" back and forth, but push hard and then draw back lightly.

Saw large and sand it down to size.