I'd like to think that maybe V'Ger and the Borg were both created by the same root race of machines, experimenting with different principles of mechanically-enhanced consciousness. They saw in Voyager 6 the "kindred spirit" of a mechanical device, however primitive, and gave it "life". They saw in the Borg, probably nothing more than a humanoid species tinkering with cybernetics at the time, the potential to be greater than the sum of its parts and acted according to the needs of the target being altered. CLEARLY the "machine planet" didn't have its own version of the Prime Directive against cultural contamination. The need for mechanical perfection and ascension through that perfection is evident in both V'Ger and the Borg and is the driving force of their individual existences. We all know the Bord assimilated other cultures to add to their technological and biological distinctiveness to the Collective. V'Ger cruised the universe, sucking up the "patterns" of whole civilizations and galaxies in an effort to know everything, ascend, attain perfection, and touch its creator. Two means to the same end. Perhaps the Living Machines themselves were looking for a way to evolve into a higher kind of life form and they used V'Ger and Borg in an attempt to attain that evolution through fundamentally different kinds of "vessels". Hell, they may have even been responsible for the Nomad/Tan Ru incident, especially since many in the fandom always felt that The Motion Picture was nothing more than a retelling of "The Changeling" anyway... Maybe that was the point!
As mentioned before, time frame incompatibility and/or rationalization is irrelevant, as Voyager 6 went through a black hole and could have appeared at any place in space and time. Only the creation of the Borg would need to have been fixed in time (but then again, I'm thinking so "three dimensionally", aren't I?). Removing the Shatnerverse POV from the context for a minute and looking at it from a slightly different perspective, I honestly don't think it's as far-fetched as some people here are saying.