They should just ignore the fines. Don't pay them, but keep paying for insurance for those employees who have been getting it all along. When the govt tries to shut them down, get REAL public with how their employees DO have insurance, and how many people will be out of work because of the government's political agenda, which is contrary to the Constitutional rights of the owners of the company.
The government's whole case is built on the argument that Hobby Lobby can have no "religious objection" because it is a corporation that is separate from its individual owners. At the rate of $1.3 million per day in fines the corporation isn't going to be in business for very long, and within weeks or months it will be bankrupt and unable to pay any more fines anyway. To the extent possible, the owners should just strip the corporation of all its assets while the case proceeds.
Their last business transaction should involve the sale of the company name and any associated trademark to one of the family members ... for $1.