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In an earlier paper of the authors, a general family of instances of therelative Langlands duality of Ben-Zvi-Sakellaridis-Venkatesh [BZSV] wereproposed and studied in the setting of branching problems for smoothrepresentations. In this paper, we show the numerical conjectures of [BZSV] forthe local Plancherel density, as well as an application to their conjectures onglobal periods, for this general family of instances.

Generalised Whittaker models as instances of relative Langlands duality II: Plancherel density and global periods