You were close with guessing FLL made this one as the Linden examples and your Infanterie Sturmabzeichen both come from the Lüdenscheid area.
Your example is attributed to the firm of Berg & Nolte, Lüdenscheid.
B&NL also made solid zinc variants and comparing the unique hardware attachment of these solids to the B&NL marked Luftwaffe examples, the connection was made. Most B&NL hollow examples encountered lack any type finish and did not stand up well with time. Yours looks to be in nice shape.
Best Regards, fischer