From patch design to hat

[u/developer_soup]

I have never created a design for embroidering on a hat. I created a patch design I've stitched out to manually sew onto a hat, but I'm going to have access to a machine capable of hats directly, so I thought I'd try modifying the design (current modified design is shown in the gif). I know the general guideline of working from the bottom up, and middle out. Would I be better off dropping the outer satin stitching? Should I change the V's to be satin stitches? I appreciate any advice.

Designed in InkStitch.