Traveling in The Warp can, in some instances, take much longer than anticipated. From what I understand months and even years (centuries?) may pass in real time during a particularly bad jump. Has there ever been any instance, either in the rules or any canon fiction, of exiting prior to when the initial jump was made?

There've been a few canon incidents. An Imperial Navy vessel answering her own distress beacon, the Tallarn had a similar thing happen in Desert Warriors . One of the more amusing incidents was an Ork Warboss hurled back in time, who promptly went to kill his past self to get a copy of his favourite gun, with no discernible side-effects. It's worth pointing out that there is an Inquisition branch dedicated to dealing with time-travelling shenanigans, known as the Ordo Chronos.

And an example where a crew were spaced and officer taken off for interrogation, for impersonating Naval personnel, because they hadn't been born yet.

There was another example where a ship (the Oceanid , under Rogue Trader Lucius van Gerrit) travelling as part of a crusade fleet arrived first at a rendez-vous after a warp jump and found the hulk of one of its consorts, which had apparently been drifting without crew for several centuries. Everyone was unsettled and moved Oceanid away from the empty vessel. Relatively shortly thereafter, the rest of the crusade fleet arrived... including the one they'd found as a drifting hulk.