If you encounter a problem with the show's premise being in danger due to tech ... then here's a way out:
They could have simply stated that their new engine suffered heavy damage that would essentially take significant amount of time to repair without access to a star-base (and making repairs on the go would be limited at best - at least when it comes to restoring full sustainable speed).
They could have incrementally increased their speed by the end of each year.
By the time they reached the Borg, there could have been some interesting scenes with the chase at high warp because the ship could hypothetically keep up and increase their speed as the story with the Borg progressed (which could further peak the Borg's interests).
Even in the regular show, it was by early season 4 that the crew started to view their situation as 'when we get home' and not 'if'.
So I really don't see the problem in how this is different with them being able to get back to Federation space under their own power (eventually, with at first being the question IF they will be able to fix their engines to the point to allow them to travel as fast).