You have 2 problems, first one is that you either have a clog in the toilet drain, or a clogged vent. I would definatly check the vent line that runs to the roof of your house, could have a birds nest in it or leaves, etc. You may also have something caught in the internal trap of the toilet which becomes lodged and dislodged. Pulling the toilet and cleaning out the trap with a snake and possibly the drain will remedy this. Here's a link to describe
http://www.toiletology.com/howitwrk.shtml
I would also either replace the entire toilet with a new Kohler Wellworth lite, cost around $100 at Home Depot, or replace the devices inside the toilet tank. Your flush valve is not stopping the water from continuing to fil up the tank once the float has reached it's setpoint, sounds like the tube that directs this water to the overflow may also be too long. This tube should be 1/4" above the top of the overflow column. Your flapper may also be leaking by and allowing water into the bowl, so please replace all parts with new Fluidmaster parts. Here's another link to describe what parts:
http://www.toiletology.com/troubles.shtml
Replacing the entire toilet is cheap insurance. Also make sure the vents and drains are clear. I would hold off reporting to your insurance company again, it will work against you, save the calls for high dollar items instead.