Great news about the new job, Duck!
What you may find is that the coverage from the employer is better coverage than the state plan.
As for "free-loading" ... I'd guess that the taxes you've paid for many years (that have funded this benefit for others) would not classify you as a "free-loader". And Luv mentions a good point ... whether there will be any penalty for not enrolling the kids as soon as they are eligible.
Option 3 ... maybe ... for the 90-day probationary period ... sometimes you can stay on your present employer's plan for a period of time and pay the premium yourself. Since you were scheduled for layoff anyhow; depending on the # of employees of your employer; depending on the terms of the contract with the employer. Although maybe you've already inquired about that? Also might check out open enrollment periods for a non-profit if you have one in NC. Some of them offer "temporary" plans for interim periods like this.