[Eliot Ness]

........I'm going to guess that Peck & Hills Furniture in Chicago bought their radio chassis from Jesse French......

Alan, Jesse French did not make their radio chassis's, they were a piano company who decided to dabble in radios for a couple of years.  Their most popular set, the model G or Junior had a Loftin White chassis made by Sterling in Cleveland, Oh.  

So while you're most likely correct that Peck & Hills Furniture bought the chassis from someone else, it would not have been Jesse French.  I don't recognize the chassis in your radio, but if you look/ask around long enough you might spot who actually made the chassis.