My take is that you have a duty to notify your carrier when you have a claim.  Check your policy for the specific language.  In my policy, a claim means "a written demand" for damages. Upon receipt of such a written demand, I have to notify my carrier "as soon as practicable."  Waiting too long could give them an excuse to deny the claim.

With regard to LLC protections, I think it depends on whose negligence it was that caused the claim.  If it was an employee who was negligent, the LLC could offer some protection for the owner's personal assets.  However, if the owner was negligent the LLC probably wouldn't be of much help.  The reason is that the claimant will probably sue both the corporation and the owner individually. 

Something else to consider is whether your state considers claims against abstractors as tort claims or breach of contract claims.  If they are contractual, the claimant could be limited to claim against the LLC with which they entered into the contract.