The discussion with Alan today helped me find a direction with my project. Departing from a rat was a good start, and one of the key pieces of advice I walked away with was that when it comes ot my source creatures, I should take away what makes them characteristic, hopefully left with something weird. Rats without their fur are quite wrinkly and chickens without their feathers look bizarre and strange.
One thing that was touched on in the discussion was lizards. I considered adding some lizard-like features and I was recommended to look at running lizards. Which move quite differently and at a very different pace from the normal kind. One species, the basilisk, has such a speed and such a surface area on its feet that it can run on water. Most of these lizards are quite small, thin and agile. And such a creature might be more familiar historically to South America than either rats or chickens, creatures that have a more familiar history in Europe and Asia. Which ties into a thought I had recently that it's far more likely "white rat with a rooster's head" is the legend's way of describing what this thing looks like. Being a by-eye interpretation, it's possible the creature looks nothing like a giant rat. Which gives some design flexibility; for one I am intrigued at giving it legs like these running lizards (which have been described as moving like a bicycle, could be interesting to animate)