@fBoyle-- I don't think that there is any pleasant way to get rid of rats. If you want them gone, you have to accept that.
Rat traps are probably the fastest way to kill rats. My landowner uses them when he suspects an infestation. We don't have any pets or small children, so it's not a problem. He puts some peanut butter on the trap and the rats go for it every time.
If you can't use traps, then definitely go for a rat poison bait. I think that the anti-coagulant ones work faster than you think. They work in a day or two at most and that's the norm for most rat poisons.
When I was a child, my dad used a pink rat poison but I can't recall the name. That stuff was so strong! It would kill the rats in less than a day! I don't even know if that poison is available or legal anymore. It was probably taken off the shelf for being too dangerous.