...Or then the Borg got exactly what they wanted: the bombardment was merely a means of luring Picard and his Chief Engineer to Montana, where they would "repair" the crazy tin can of a madman into a working warpship and thus help create the utterly unlikely Federation which in 200 years would provide such bountiful pickings for the Borg.
Or then the Borg really were off to kill Cochrane and destroy his ship, but they were discreet and wanted to use weaponry that could be mistaken for 21st century ECON ordnance. It would do the job in an hour or two, without suggesting extraterrestrial intervention.
As for time travel hurting the time traveler, it could be argued that the E-E lost her shields and sensors when the Borg tractor beam hit her, much like the E-D shields were always drained by Borg beams. There's no dialogue to indicate that the damage would be the result of time travel, to be sure.