Any recommendations for a standalone insurance that would let me choose a different replacement diamond (or cash) instead of finding an "equivalent" one?
Check with the carrier of your homeowners or tenant policy to see if they can write what's known as a floater policy (inland marine). Many carriers do this. You can either schedule individual items or insure a class of items for a blanket amount. For example, you can insure jewelry, guns, furs, cameras, stamp collections and valuable antiques on such a policy.
State Farm comes recommended for this. From what I understand, they have been insuring jewelry and individual pieces that are of certain value for a long time now.