I always used to be confused by "A stitch in time saves nine," but now I know it means that it's better to fix a small tear with one stitch than to wait until it's big enough to need ten stitches. So if you stitch the tear "in time," you save an additional nine stitches. In other words, it's better to address a problem while it's small and easy to fix than to neglect it until it becomes harder to fix.
I can see the connection to "Better safe than sorry," though, because that means it's better to take action against a possible problem than to neglect it. That's more about whether you address it at all than whether you put it off for later, but I guess they overlap.
I don´t know if it has anything to do with Garak´s "A stitch in time".
Cardassia didn't address its problems in time, and now it's left trying to repair the mess. Garak himself left all his wounds and tears unaddressed until he had to confront his entire life in the aftermath of disaster. Now he has to make sense of it and piece it all together, just as Cardassia must repair itself.
Lots of stitches needed now.