Just can't get the hang of sewing non-structured hats, any advice

Use a backing designed for caps, stiff tearaway and double up if needed. Digitize to sew from center out and a maximum size of 2.5 high and 4.25 long if able. If you are doing a 6 panel with a center seam sometimes if you digitize a satin stitch to cover the seam the field atop that seam will smooth out. Properly hoop your hat to avoid as much flagging as possible and test sewing speeds for the best results. We use 80/12 teflon or titanium coated needles for all hats, the larger needle will not deflect as will the 75/11s and smaller.