Hi dl74075.
I don't have a positive ID for you guitar but I do have some initial thoughts. You Kay reminds me of archtops in their "Television" guitar series produced in the late 1930's. The Kay logo was not used until 1936-37.
Compare your guitar to this K-52 Television guitar:
Not an exact match, but certainly similar.
Here is Michael Wright's chapter on early Kay guitars you might find interesting. He discusses the Television model. Hopefully, Forum members can contribute more information about your instrument.