3 cats + 1 rat = ?

You'd think it would be pretty straight forward.

We're in heavy duty stuff-purging mode. The piles are growing. We've purged roughly 100 books, the same number of movies and slightly fewer video games. Trash is going out in bundles. A rather huge pile is forming for donation. Thom over at Sparky's is involved in several charities and is willing to send over his truck to pick up our donation items as well as all our leftover consumables.
Of course, to put things in order means creating a path of chaos. Our bedroom is always the dumping ground and the last place to get any attention. Suitcases from our trip, piles of clothing, rolled carpets, boxes and bags of, well, I'm not sure... but anyway, it's a veritable playground for all things small and furry aside from the fact that is probably all reeks of cat. Ian was in the bedroom yesterday afternoon and called me over. We had a mouse and it had just run into the bathroom. It came up through the drainage drain behind the toilet which Ian had now stuffed a toilet scrubber into until something more permanent could be arranged. Usually the drain has a metal sieve on top and it was neatly pushed aside. I didn't see the critter but had no doubts it was around.
This morning, we both saw it in the bedroom. It was no mouse but a rat easily 5 inches long, with another 6+ inches of tail.
Well, we knew what to do with that thing:
Shut the bathroom door
Shut bedroom door
Grab 1 cat... another cat.. a third cat...
Toss three cats in the room with the giant rodent.
Wait.
A couple hours later we checked on what was going on. We hadn't heard any meowing, no rat shrieks, nothing falling off counters, definitely no suggestion of a mighty chase.
The cats were all hiding under the bed. We gave them more time.
A couple hours later, one is still under the bed, another is warily sniffing around, and the other is sleeping on the dresser.
These felines would fail miserably in the wild. We released them back to the rest of the house, acquired a sticky pad mouse trap, placed it in the bathroom between the door and the drain and left.
Success. The rat had gotten itself so stuck it hardly seemed to be breathing, which was a good thing since the next step was to drown the poor thing. These sticky pads are roughly in the middle between a killing machine like a classic trap and a life preserving cage trap. They catch the animal in a thick sticky slimy goo that is impossible to remove without heavy doses of vegetable oil and a thorough scrubbing with soap. Needless to say, not going that far to rescue a rat that invaded the house. But it also doesn't kill them. So we're left with an alive creature that is impossible to release. Drowning is quicker than starving and it seemed that it had gotten so gooped up it didn't squeak once as it's head was stuck too.
Ian did the dirty deed. Now, we assume the critter hadn't already invited his family to move in.