According Fraser-Lu, the fine, pierced ivory carving is a style characteristic of Lower Burma, originating in Moulmien (just above the Malay Peninsula) but now done in Rangoon, the Moulmien industry having died out. Fraser-Lu, "Burmese Crafts," p. 114. According to Egerton, ivory carving in high-relief was a Shan style. Egerton, "An Illustrated Handbook of Indian Arms and Those of Nepal, Burma, Thailand and Malaya," p. 85. This, of course, does not tell us whether or not a high-relief carving style is/was found further south, but many (if not most) of the non-pierced, high-relief handles I have seen are on Shan dha, and the pierced styles on Burman dha.
Shan dha

Burman dha