Let this be a lesson...

Oh, I have another humane design involving a coffee can, a screen and a rat trap that I found online which also works, but the cardboard one is just way easier... Involves no assembly and pretty much zero possibility of an injury to the rat, whereas the coffee can with screen top method could conceivable snap shut on the rat's tail.

Would a standard, plastic tall kitchen trash can work or do you think they'd be able to grip with their claws and climb out?
If I don't have to poison it/them then have dead rat(s) somewhere in my house, I'd rather not. :)

Should work! I just used a standard platic bathroom one for my mouse.

Plus, you may also hear it fall in, in which case you just go and get it right away...

In all seriousness, I've never had to wait more than 4 hours to catch one.

And the inhumane trap reluctance I understand... My old landlord put one in my fruit cellar once without me knowing (I just told them I had mice)... I walked in one day to a tail hanging infront of my face and had to call the boyfriend to remove it... Then about 4 weeks later there was an odd smell in there... Turns out he'd hidden two traps in the same spot and I didn't know... Again, thanks to the boyfriend... I was angry with the landlord, was just going to go with humane options.

Oh... I've also used our extra 20 gallon aquarium, it works great :)

I have one of those but it has a 10" tarantula currently residing in it. :D
I have a lot of standard 10 gallon tanks but I don't know if those would be tall enough that a rat would not be able to get out.

What's the height on them? Contrary to some belief, rats aren't really the greatest jumpers out there...

Look at all the people on the feeder page who have a couple stowed away in uncovered tanks! As long as there isn't something he can climb on, you should be good.

The 10s are 12" high