Blue Cross Blue Shield will not insure full timers in SD,NH,and many other (all?) states. The only exception is if you have an existing group policy provided by a employer or governmental (state/federal) entity as a pension benefit.
BCBS requires proof of an actual address (a mail forwarding service street address will not work) and physical presence in the state for six months or more each year.
Before we reached Medicare age we used a policy from Assurant Health now owned by Time Life. We had no claims so don't know how good they are in that respect. The cost was high - about $1800 per month for the two of us.
We used an insurance broker next door to our mail forwarding service(Alternative Resources ) to get quotes from several companies.
Dougherty & Associates. 3704 S Westport Ave, Sioux Falls, SD 57106. (605) 361-6318.