I checked Expedia for reservations and they said there was no availability. I then called the cottages and was told that they do, indeed, have vacancies for the dates I want, but they don't use Expedia. I think it is amazing that Expedia can say there's no availability instead of admitting that they aren't permitted to book reservations for this property.
The cottages' numbers, per MSN YellowPages, are:
(888) 757-0015 (toll-free)