Sorry cannot help directly but crown in wreath had three iterations:
first: for the very most senior tranche of army warrant officers as then was: Conductor c. 1899, then staggered over a few years for his equals, the First Class Staff Sergeant Majors and the Master Gunner First class [all by 1915],
then with the major revision of October 1918, when those at RQMS level adopted the badge to distinguish them from other WO Class IIs,
and finally from 1938/9 for WO Class IIs during the period when the short-lived rank of WO III existed [crown only] until it quietly withered away during/ after the 2nd World War.
NB during 1915 to 1918 the badge structure had crown and wreath senior to the Royal Arms, very odd-looking to modern eyes. The 1918 sequence has seen little change, in essence, to this day, although several levels have been added at the top.
But RAF: not as far as I know.
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