A very different kind of Borg (although never referred to by name, as in ENT: "Regeneration") already appeared in the prequel novel Starfleet Academy: The Delta Anomaly
. It was some kind of advanced scout hiding out in San Fransisco, and made some very interesting use of it's nanotechnology.
As for bringing the Borg back to film, I'd love to see what CG and a big budget could do. No longer would the Borg be guys in rubber suits and make-up, but using CG, body parts could be replaced or removed. Imagine a Borg drone without a bottom jaw, with moving machinery inside his torso, stick thin atrophied limbs skewered with machine parts. Steampunk zombies.
As for why they would be interested in the Alpha Quadrant "early".... maybe long-range Borg sensors detected the temporal distortions upon Nero or Spock's arrivals. Or maybe Narada's Borg-derived technology (see: Countdown
) sent out a homing signal. Any excuse could be made, or extrapolated by fans.