Missile modules are the best thing for taking out starbases and the Ravenous Shadow. Beam weapons are also very effective at melting bases, since they don't dodge.
Doom Accelerators, Polarizer, and Impulse Reactor modules should all do extra damage to starbases and the Ravenous Shadow, there aren't any small modules that have direct hull bonuses against ultra heavy but those modules have indirect damage bonuses.
Note that everything in the nebulas is immune to paralyzation, translocation, and reclamation, so those small modules will not be useful (though paralyzer modules have unusually high base damage).
I usually save right before entering a nebula, then reload and go unlock and equip whatever modules seem like a good idea. Large starbases can also help you module swap. If there's one present, it can almost instantly restore any force field modules you have equipped that have been destroyed; they're super slow at restoring champion hp, though, so be careful.
