I believe the AMA insurance will cover you anywhere (within reason) you fly as long as you abide by the safety code and follow it to the letter. Note, under the General rules, paragraph 5 about personal ID in the plane. I think a lot of people don't do that. Also requires your AMA number on the plane, another thing a lot of people forget to do. The 3 mile radius for flying may be the only true restriction to private field flying. But, just to be safe get the answer in writing from the AMA.
Deaths, don't recall one for a couple years. I think the last one was when a man got hit square in the chest with a plane and that killed him. Years back there used to be a lot more of that regarding serious injury and deaths when involved with Pylon Racing but rules and protection cages have resolved most of that. It's quite a site to see a 5 pound plane hit the ground or go through a tree at 180mph and a motor screaming at 40,000+ rpm. The silence after a crash is deafening. I CD'd a quarter final plyon race for the NMPRA once and I vowed to never volunteer for that again. You can check the safety code at the AMA web site: www.modelaircraft.org and go the the heading "membership services". Actually you may have gotten a copy with your AMA membership. Last, insurance payouts. There have been a number that have gone to the limit of homeowners plus AMA. Seems to me there is still a BIG one that hasn't been settled. That is the basic reason for the sizeable jump in AMA membership dues this year. Partly because of the obvious insurance cost increase and a little extra was factored in as a fudge against more increases that everyone knows will happen. We have to let the trial lawyers make a living!!!
Hope you get a favorable answer from AMA.