Q:

How to mobilize Cardinal Koth?

From The Shadow Rune campaign, The Cardinal's Plight quest, Encounter 2:
Special Rules extract:

Once rescued, at the end of the last hero turn each round, Cardinal Koth performs a single move action. Koth cannot perform other actions.

The Overlord gets a master zombie, and if it dies he can reinforce it at the start of his turn. Assume the master zombie is always next to Cardinal Koth. The master zombie has Grab:

Choose a hero adjacent to this monster. The hero must test Might. If the hero fails, he is Immobilized.

Cardinal Koth has a Might of 2, so with our assumption it's safe to say the master zombie will almost always immobilize Cardinal Koth.
And, for completeness, Immobilized:

You cannot perform move actions or suffer Fatigue to gain movement points. Discard this card or token at the end of your turn.

How can this Overlord strategy be countered?
Once mobilized Cardinal Koth can outpace the master zombie, but situations like respawning the master zombie at the entrance or the Overlord playing Dash could immobilize us again.
Ideas:

Stun (don't kill) the master zombie. Then wait (forever?) for an unlucky roll.
Blockade Koth in a corner. Have to move him to a corner first plus minimum three heroes.
Use a search item to remove the condition. Requires lucky searching.
The quest rule that he gets a move action trumps?

Page 18, "The Golden Rules": The first bullet point should read,
  “Some cards and abilities come in direct conflict with the rules found in
  this rulebook. Cards and abilities take precedence over the rules in this
  rulebook. Furthermore, many quest rules listed in the Quest Guides come
  in direct conflict with cards, abilities, and the rules found in this rulebook.
  The quest rules listed in the Quest Guides take precedence over cards,
  abilities, and the rulebook.”
-Descent: Journeys in the Dark Second Edition Errata and FAQ Version 1.6

I'm thinking there might be abilities or feats that can take care of this, but I'm not familiar with all the classes.

A:

Summary
Cardinal Koth can still take a move action while immobilized because the quest rule trumps the card effect of Immobilize
Explanation
If the master zombie can prevent the cardinal from moving with grab, this is basically impossible for the heroes unless they have some of the special things I've listed in the "Hard Mode" section below.  The cardinal has a 22% of resisting a grab.  Because the master zombie can spawn next to the cardinal and grab twice on it's turn if needed, the heroes have a 5% chance of being able to move with the cardinal on any turn (assuming the overlord uses grab as much as possible).  Even if the heroes managed to win this way, it would be extremely tedious.  As a result, this can't be the way this scenario was intended to work.  The cardinal must be able to move despite the grab ability.  What follows is the rules lawyering to achieve this.
The rules for Cardinal Koth read differently from the rules for other special hero characters in that Koth never activates:

Once rescued, at the end of the last hero turn each round, Cardinal Koth performs a single move action.

Compare this to the very similar special character Fredrick in The Monster's Hoard part 1:

Fredrick activates at the end of the last hero turn each round...  When activated, he performs only 1 move action.

Every other scenario with a special character for the heroes (villagers, guards, etc.), these special characters get an activation... except the cardinal.  As a result, I believe that the cardinal taking a move action is covered as a special rule of the scenario and thus trumps the restriction of Immobilize.  Essentially, because the move action is not done as part of an activation, it is the scenario that is causing Cardinal Koth to move, not the cardinal himself, and Immobilize restricts the cardinal and not the scenario.
Why then does the cardinal have attributes at all?  Because he can still be poisoned, thrown, etc.  He can even gain the Immobilized condition, it just usually doesn't do anything to him.
In particular, the scenario rule allows the cardinal to ignore the You cannot perform move actions portion of Immobilize.  That's it.  The cardinal can still have his movement affected by other things, such as the overlord card Tripwire.  The cardinal can still be blocked by zombies or other monsters standing in doorways.  He can even have his movement interrupted by Web Trap, since, according to the FAQ, becoming immobilized reduces your current movement points to 0.
I have played under this rules interpretation and it works fine.  It is still quite interesting tactically, and I assume is what the scenario designers intended.

Hard mode
You can play this scenario on hard mode, where the cardinal can't move while immobilized.  In this case, the heroes need special techniques or to have found a particular item in order to have any real chance of winning.
Curse Doll
If you find the Curse Doll as a search item, you can get the cardinal to the door of the library (the Curse Doll is a one-time-use condition remover).  Make sure the master zombie is still alive put 2 heroes blocking the library spaces behind the cardinal, thus preventing the master zombie from moving next to the cardinal and also from moving out of the library.  Then, you can just leave two heroes there the doorway of the library to keep the master zombie trapped and move the cardinal out.
Disciple/Apothecary
The Disciple class has Cleansing Touch which can remove immobilize:

Each time you use Prayer of Healing on a hero, that hero may also discard 1 of his Condition cards.

While the cardinal can't recover health from Prayer of Healing, he can still be targeted by it for the purpose of cleansing touch.
The Apothecary has a similar ability.
Wildlander
You can use the Wildlander's First Strike ability to kill the master zombie at the beginning of it's activation:

During the overlord's turn, immediately after he chooses a monster to activate, you may exhaust this card to perform an attack targeting that monster with a Bow. After this attack is resolved, if the monster was not defeated, it may continue its activation. 

Stun
If you can reliably stun the master zombie (such as with a hero ability), the master zombie can only grab once and can't attack.  Within 5 turns, this will give you an opening to make a break out of the library and outrun the master zombie.

Other alternatives
There are many other house rules you could introduce if you wanted this scenario to be winnable by the heroes but still prevent the cardinal from moving while immobilized.

Have the zombie spawn at the end of the overlord's turn instead of the beginning.  Then, the heroes can kill the master zombie to buy a turn of respite and get the cardinal out of the library.
Zombies only spawn at the entrance.  Then, the heroes can kill the master zombie and block off the entrance to hold off the zombie hoards while they move the cardinal into place for their dash outside.  It's far more cinematic this way too.
If the heroes defeat all of the monsters, consider that an alternate victory condition.  It's kind of silly that the heroes don't win by default if they do this.
Only allow the master zombie to make one grab at the cardinal per turn.  This gives a 22% chance of the cardinal moving.
Give the cardinal 3 strength.  This ups him to a 53% chance of resisting one grab, meaning he now has the quite reasonable 28% chance of resisting a double grab.

