Interesting thread. I agree with Paul and Emerson. I have rats and mice. I guess most people know that poison is not a good idea: dead smelly rats that are not disposed of, dogs eating poison and a big fat vet bill to try to save them.
One thing I have learned is that rats and mice are an on-going problem. Dogs are a great solution because eventually they will find the baby rodents and have a feast on them. I wonder how many rats an owl would eat? Does your homeless guy have friends who have dogs?
I also have snakes going after my rats. They shed their skins in my attic (3d floor) so they can climb -- these are Alabama black snakes--they get quite big and can be awesome if you encounter one. It definitely is a thrilling experience! I bet your local one's do as well at catching rats.
I would try to find a source to determine a number of predators who would not be too incompatble with each other. The dogs may go after the snakes for example. The snakes here are quite aggressive and will fight a dog. [They are not poisonous so it is just entertainment for both of them].
As for people, what is a park for if its not to introduce people to wildlife? They should know that the snakes are there, that the snakes are not poisonous and what kinds of snake behavior they are likely to encounter.
If you can't buy snakes, you might get some help from the boy scouts or similar groups who can collect some for you. I was manager of a 16 acre historic site here. We had poisonous snakes in the basement of an 1830s kitchen. A very old guy told me how they used to do 'snake hunts'. They get a lawnmower started and run it down in the building. The snakes do not like the vibrations. Then several men surround the building with croaker sacks (burlap bags).
They have sticks to direct the snakes into the sacks. Then you would have sacks full of rat eating snakes. Just take the snake catchers to the park for a picnic and give them a lifetime pass!
In buildings I have an electric rat zapper. It runs on batteries and catches just one at a time. Then you have to dispose of the zapped rat and reset the trap. You have to clean out the residue left by the dying rat periodically. Recently I bought another rat zapper so I have two. I am now catching mostly mice rather than rats. I suspect some of your rats will leave on their own once there is more activity in the park.
Rat snakes:
http://www.outdooralabama.com/watchable-wildlife/what/reptiles/Snakes/ratsnake.cfm Here is an article on predators (besides rat terriers) that feed on rats. Owls are apparently a very good choice because they are nocturnal and feed when the rats are most active.
http://activism.suite101.com/article.cfm/animal_control_for_predators_but_not_for_pests