Unless you had lots of manure to till in along with the paper it would not be good for your soil, or any plants, to till in that paper. Tilling paper into the soil would result in all available Nitrogen to be used by the soil bacteria to digest that high carbon material. Rather than shredding the paper you could lay it on the soil and cover it with shredded leaves, something you should have lots of in Pennsylvania, and that would help your soil and not hinder plant growth.

I'm not totally sure why you don't just recycle the cardboard. Your kitchen, trees, etc. should be able to give you as much compost as you need. Recycling is better for the planet as fewer trees will need to be cut down and less energy is used when recycling than logging. If you want to compost it, why not recycle it then buy tissue and paper towels made from recycled paper and use that as compost, this was the maximum value is squeezed from all the trees that are cut down to make paper.

Yea it's totally stupid to throw good food away, and even worse throw good compostable food and cardboard to the dump when it could be the food for worms which supplies the castings to fertilize food for people. Will Allen, founder of Growing Power uses just such a method to make compost with worms, that he feeds to fish that he grows in Greenhouses with plants fish and worms in an integrated growing system in downtown Milwaukee and Chicago. He produces tons and tons of food with urban trash, worms and hard work. Know anybody at Publix I can talk to to enlighten them? Ren Here is a link that might be useful: Growing Power Vermicomposting

We have a paper shredder from OfficeMax that I run all our pizza boxes through. Just have to tear them into pieces narrow enough to feed into shredder. It's not a cross-cut model, so I get long strips. My worm "bin" is a large terra cotta planter the landlord left behind. I've got it on a small balcony off the kitchen, it gets afternoon sun but is protected somewhat by the wall and the thick terra cotta. I feed them a blender slurry which I pour into a hole in the cardboard layer and cover back over with the cardboard. By the time we have more pizza boxes to shred, the old ones are pretty much incorporated. Only problem is fungus gnats, I keep a piece of screen over the top to hold down the swarm. Eventually I plan to put a tree or shrub in there and start another one.