I'll just chime in here on some observations of the cellar missions. I've fought it 5 or 6 times and only had a blocked section spawn once. It does take several turns of pickaxing to get through.
Saving cats is kind of a roll of the dice. I've had the cats spawn right in rat clusters and go down before I ever saw them. Other times they were safe no where near the rodents.
Despite the trouble reported with melee, the rats are super squishy. The best tactic I can suggest is showing up with the fastest firing shot guns you have. Even Ol shotguns work great, but domestics, mil shotties, and best yet combat shotguns, street sweepers, or assault shotguns. These all do wonders on the rodent problems. Bring as many gals as you can with shotties and you will do fine.