We have actually set up our insurance coverage to be full replacement value, rather than fair market value. So check your insurance policy to be sure.
Otherwise, I agree completely with Spirit Deer's comments and suggestions. When you are making the video, be sure you use audio and go around the room opening every cabinet door and drawer, showing everything in there, including audio notes such as history of the item or anything that makes it unique or more valuable (antique purchased at such and such a place, signed original, new custom cabinetry we installed after we moved in, etc.). Start in one corner of the room and work your way around clockwise (or counter, but be consistent) and be sure to show the upper levels (did you install a new chandelier or lighting in the bathroom?) and the lower levels (did you change out the carpet for hardwood floors?). Go through all rooms in the house including storage like attics, basements, sheds, garage.