I had never heard "in the essence of time" before a recent trip to Virginia. Various local attendees of a meeting I attended used the phrase to justify moving on to a new topic, in a situation where I would expect to hear "in the interest of time."
It strikes my ear as a malapropism, and I agree with the theory I found (the first Google result when searching the phrase in quotation marks):
This subtle malaphor is a mix of “in the interest of saving time” (in order to save time) and “time is of the essence” (meeting the deadlines is essential).
That said, language is certainly known to evolve, and there may be more happening here than I recognize. I'd be interested in a more detailed explanation, especially if someone has a reasoned argument for this phrase being useful, meaningful, or in wider use than I'm aware.