You can probably reserve an entry now for June 1 at   (You need to Login or Register but I'd suggest letting your outfitter reserve a Stanton permit.

You can also check availability on the site for any date and entry. Remember though, there are resident and non-resident quotas. I think it's three days out that that distinction goes away and it's just another paddler getting a permit. I honestly wouldn't sweat availability, especially for a northern entry.