Insurance - Moving property from personal to LLC

I purchased a rental property in my personal name and want to move it over to my LLC. The insurance payments are paid by the lender from my escrow account. In speaking with my current insurance co, they won't insure the property going forward if it is not in my personal name as they don't insure property owned by an entity. I want to change the insurance provider and name of the insured to my LLC, but since the insurance is paid by the lender, how do I do it without accelerating the due on sale? I am hoping that I am over thinking this and there is a simple answer that I am missing so please share your thoughts.