Perhaps the parallels between the timelines say that the Federation didn't take the war as seriously as it should have in the early stages, so they focused just as much on exploration as they did in the prime timeline
The war might have been relatively low intensity for most of it's history, something like the ongoing board war with the Cardassians. When the Enterprise was in it's final stages of construction, and the the senior crew already assigned, the war increased in intensity and the Enterprise's designation was changed from multi-mission explorer to battleship.
... Picard was afraid Starfleet would collapse in 6 months or so.
I wonder about this statement by Picard. Captain Garrett had just informed him that she had no intention of returning her ship and crew to their orginal time period, and to face near certain death. It was only then that Picard told her that the Federation had "six months" before surrender.
Picard wanted her to go back and prevent the war, but he really couldn't directly order her to do so, he needed her to return voluntarily.
Was Picard lying? I think he might have been.