Another vote for National General (formerly GMAC). Saved me significant dollars when I switch a couple of years ago. Renewal was almost no change.
And yes, if you call and tell them the rig is in storage (doesn't matter where) they will reduce your premium accordingly. When you take it out of storage just call them again and coverage is back to normal.
Do not have any claim experience but have had contact with them for general issues and questions. Always got a person on the phone in reasonable time and good advice and/or info.