I just turned 21 on Tuesday and one of my favorite birthday presents (besides my older brother taking me to his favorite pub) was the Son of Stitch n' Bitch book, and I can't wait to try double knitting

I want to use double-knitting to re-start a partial intarsia hat I frogged this morning. After I made several sample swatches and two fairly plain hats, I finally got the hang of basic intarsia. My first "nice and neat" intarsia hat was black and had the old-school Batman oval logo on the front for my friend Derek, a huge Batty fan. As I gave it to him, he mentioned that he never has enough sturdy winter hats.
I told Derek I would make him a few more, and for the first one I came up with an intarsia pattern of my own design. The shape is a basic knit-all-around hat with some K2-P1 ribbing at the beginning, plus the pattern of course.
THIS IS THE HAT I FROGGED THIS MORNING AS MENTIONED ABOVE. Over 120 stitches, the entire pattern repeats twice, once in the front and once in back. My biggest problem is that for the first 3 rounds or so, I only have maybe 3-5 stitches stretching out over the entire round! I figure double knitting it instead will help hide these annoyingly long floats and maybe not itch Derek in the head so much.
So my question is, would I--for the double knitting style--cast on 60, 120, or 240? Once I figure that much out, I can always adjust my pattern as necessary.