I have stayed at Crazyhorse in January many times. They always seemed to have a few empty spaces in various areas of the CG, even on the beach front. They also have what they called an "overflow" area near the lagoon and boat launch that usually had empty sites when everything else was filled up.
I have also stayed at the Islander. After the 1st of the year, there were very few empty sites all winter.
I don't know anything about the Beachcomber.
I was suggest calling Crazyhorse as soon as possible. They were good about trying to find a site for short term guests.