I think you're not quite correct about this (never RZM). It is listed as "altes HJ-Abzeichen"
with an annoucement in the Mitteilungsblatt der RZM from June 9, 1934 as one of the
most important, official authorized badges (parteiamtlich genehmigten Abzeichen). It is
noted with page 3.
A far as I know the badge should have the RZM marking/code since mid-1934 and was
allowed to be worn with the brown-shirt; the one worn with the headgear - so the earliest
version - never should have this RZM code. For a while it was a sort of traditions-insignia.
Later in July 1934 the traditions-Litze was introduced.