Â* I recently queried my
insurance company about coverage when my flight review expires at the
end of this month and they told me that I would have no coverage.Â*

Interesting, my policy appears to have words to make it ok if the FAA makes it ok, but talking to the company seems wise.

A) While the aircraft is in flight it will be piloted only by the person(s) specifically named as pilot(s) for your aircraft listed below, provided that the pilot-in-command has:
....
if required, a current and valid FAA Medical Certificate;
if required, a current and valid Biennial Flight Review;
....