Thanks for the report!
When I kayaked there several years ago, the registration office in Two Harbors told me Parsons Landing was completely booked. I told the young lady she could either take my money or not, but that I probably wasn't going to be paddling back to the mainland that day.
And of course, Parsons Landing was nearly empty--there were only two other tents on the whole beach.
Things get a little loose in the off-season, but there's still the chance you'll run into a ranger who'll want to see your permit.