Go with a dry bag, partly to keep sand and grit out of your pullies, as well as to keep your rope dry.
I would recommend keeping your wrap kit easily accessible.
Sure, if you have a wrapped boat you'll be there a while anyway, but I have needed the long line from a wrap kit before to get to a swimmer stranded on a rock, with daylight going away soon, and hypothermia a threat.
Or what if your boat was wrapped, and no one else had a pin kit? Or you were solo, and needed to re-flip your boat with a bunch of multi day gear on it? Or you needed it for a foot entrapment.
My belabored point being, ya never know when you'll need emergency gear, or how fast.
We can't always agree, but we can still be civil to each other.