Additional coverage: Taping a piece of pliable plastic to the shield creates a bib that will provide extended coverage.  It can be cut to fit your needs and should be attached using tape that will not leave a sticky residue.  Garbage bags and light weight plastic drop cloths are a starting point.  They will not be as durable as the shield so use them accordingly.

Protecting the brim: Covering the brim of the hat with tin foil or plastic before installing the shield will help protect it.  This covering should be discarded when you separate your hat and shield to sanitize them.