The real way to spice up anything in a game is to give it some more flavor. Instead of merely escorting the princess through the forest, she's injured and needs medical attention beyond what the players can provide, and there's a rival kingdom seeking to take her for ransom. Give it more than just a "Do this." feel, give it a "Do this, quickly, or else things might go wrong." Better yet, when you're doing this, don't have plans that are contingent on a certain outcome; the players are traveling with the princess because they have a mutual destination, nobody knows they're doing it and they'll be at worst under a little scrutiny when it turns out that she doesn't arrive.

Alternatively, play counter to their expectations; they see someone lurking in the forests and it turns out that they're refugees (bonus points if the players attack without positive identification). They think they're escorting a merchant, but they're stopped by Imperial guards who ask why they're traveling with a known smuggler and massive amounts of contraband. The merchant wanders off in the night. The merchant turns out to be capturing them for a bounty. The merchant is actually a greater demon who will eat their souls in the night. The merchant has actually been a cat all along, and can't sell anything at all. The merchant decides to turn around and go home, but the players want to go where he's going, forcing them to choose between getting paid or making progress. The bandits turn out to be former allies of the player, and the merchant turns out to be a scumbag. The bandits turn out to be scumbags, but the merchant is worse. There are no bandits, but instead spirits who are upset with the merchant in particular for desecrating a holy site (preferably one sacred to a player character). The merchant catches a disease. The players contract diseases. Disease kills the merchant en-route. The merchant turns out to be bankrupt, and this discovery is made mid-journey. The merchant is transporting slaves/contraband/other things the players morally object to. The merchant is a terrorist. Give the players a moral choice; the merchant or an injured person needing assistance. Don't make escort quests solely dependent on escorting-flexibility and dynamism are key.

Sometimes, however, stuff's just going to start to feel bland. It's the eightieth escort quest, the tenth world-threatening dungeon-dweller, and the seventeenth damsel in distress, and the players need a change of pace. Be on the lookout for alternate story hooks; defense missions, for instance, to steal a reviled video game method, actually make decent tabletop scenarios. Have them look for something out of the ordinary.

It's not really the journey that matters, it's how they get there.

A candy filled doom pool with players taking variable amounts of candy every action.

In our 4e game, we faced a countdown timed by a bowl filled with candy. Since you've obviously ruled out mapping out the entire ship and having them move through it, instead, start the timer by pouring candy into the bowl.

For every action each player takes, have them take a few pieces of doom candy, to represent "the clock ticking down." They run out of candy, bad things happen. (My recommendation would be to start the explosion on the far end of the ship and have it ripple up, just to give them an unstated grace period.)

The beauty of the doom candy is that you can adjust (slightly, but still adjust) the tension by costing out different doom counts. They fail a roll: they still succeed but they take more candy. It's a race against candy time, and since it's so tactile and visual, it has an immediate impact on the game.

Just make sure the doom bowl is appropriately impressive.

It is also important to note that running is the medium for the activities, not the activity itself. Activities should be "I try to find a shortcut on the computer" or "I force that bulkhead hatch open" or "I leap over the stocked equipment." Running is presumed, it is the successes and complications during the run that make things interesting.