The point here is that he cannot safely add any more supers. Last thing you want to do is drop a super full of honey, or tip your hive over getting one off.
Freeze is fine, but I'd just leave it in the freezer until the day before you can extract. Let it warm up in a sealed container, but do not wait more than a day to extract. Only takes 24 hours for wax moths or SHB to start in on it, with the result of leaking honey and a big mess, to say nothing of larvae in the honey. I've seen it, it's not pretty.
I know what you mean about too many supers -- I just put a fourth one on my hive, and am thinking about another one, and the last one is higher than shoulder height. At least 100 lbs of honey in there already, and they are still flying like mad! A good year for once, eh?
Too bad I only have one hive in production, although a big flow is great for a package install too.
Peter