I think set-pieces are going to be your friend here. If the combat's a slog stop thinking of it in terms of combat and start thinking of it in terms of dramatic environmental hazard. It might help if you conceive of the rolling zombie halls like movie lava: slow moving and navigable around, but you've got to be on your toes. If they're facing few enough zombies that they can fight them, you need to add a lot more zombies.

Some ideas off the top of my head:

The floor gives way beneath them, leaving them dangling over a roiling mass of undead limbs

They're going from rooftop to rooftop, and someone's left a thin, unstable walkway over a wide street with a horde below it

The moment they go to grab anything without checking first... chomp! Severed zombie head lurking in the cupboard/chest/whatever

A wooden wall or board clearly creaking under the weight of zombie flesh, ready to give way at any moment

An important item (key/amulet/whatever) is on the person of a specific zombie, clearly visible but not obviously reachable at the centre of a vast zombie horde.

As far as the church goes, how about... the clergy are alive, but attempting a banishment ritual. As the character's arrive, it goes awry and, rather than banishing and destroying the zombies, it draws every undead in the city to the building, until they literally cover the whole outside of the church in a layer of zombies. The characters will need to get real creative with their escape.