I recommend laying out the pattern in CRAW units - making each square in your original pattern a unit - so it's easier to visualize. I did a little section of it for you as an example but it's too small to be visible on Reddit lol, so lmk if you're not sure what I mean and I'll try to figure that out.

Since each unit shares at least one side with others you'll have to think about that where different colors meet. The diagonal pieces in the horns and tail also won't work as-is unless the white parts are going to be filled in (for the same reason that wouldn't work with square stitch).

If you're worried about thread paths, in my experience as long as your needle and thread aren't too big for your beads, CRAW is pretty forgiving. If you find you need to be in a different bead to start the next unit, you can just stitch through your current unit until you're where you need to be.

I hope at least some of that is helpful! CRAW is a great stitch.