I have checked with the person who lives in the Mammoth ski house where my son has a share. The shareholders use it almost exclusively on weekends. It is definitely available any of the midweek days of the Gathering week.
The downstairs room has 7 beds, a bath and a pellet stove for heat. Bedding can be made available with a few days notice. Price is $30 per person per night max, and it could be $25 or less if several people come for multiple nights.
I have now talked to 4 people who have skied Mammoth in the past week with favorable reports from all. All lifts and 80+% of terrain are accessible. There was no rain after the big snowstorm so winter packed powder conditions prevail on at least 2/3 of the mountain including nearly all of the off piste steeps. So the invitation is officially open to anyone who wants to come down for a few days of the Gathering week at a very reasonable price.