That mysterious first verse of Gita Govinda

The first verse of the Gīta-govinda has been a source of confusion to scholars and devotees probably since it first appeared. There are a number of problems with it, all of which can be summarized as "it does not fit" what we know about the Radha-Krishna story in any source, Puranic or folk, prior to GG. Moreover, it seems to have little to do directly with the rest of GG.