Alternatives to shreders

Hey all, I have an idea that I want to share and open as a topic for discussion. I have practicly unlimited source of cardboard and want to use it in the garden as mulch but also to implement it in the soil to make it looser. I have clay soil and its very hard to work on, it is very dense, just hard to work, I believe that implementing some natural material to rot inside, will make it better. So, I have no paper shreder but I thought that if I wet the cardboard, cover the soil with it, maybe even two-three layers and use the tiller, it will shred it and mix it with the soil. Any opinions on this is much appriciated.

I have been playing with this concept for a while.
In Australia we can purchased gadgets that split the cardboard so it become pliable enough to used a loose packaging.
I causes the cardboard to have lots of slits. These make it easy for worms  break up when under the soil.

Cardboard is a great way to solarize it to kill weeds and also as mulch, as it will hold the moisture and let microbes do their work.  However, the microbes need minerals and humates to feed on.  Gypsum (calcium sulfate) will soften hard pan soils such as clay.   Also baking soda will floculate hard soils and make them soft.  The microbes live the calcium in gypsum or calcium as carbonate (lime).  

I have heavy soil. Just keeping it covered (with cardboard, or any other mulch) makes a big difference in its workability, plus kills the weeds. A single layer, overlapped, at the edges, is about right for me. I weigh it down with old boards and rocks. I try to cover it with other mulch when possible, and it pretty much disappears by the end of the season. my source is limited, so I only use it for the weediest sections of the garden.

Bonus is to spread compost (raw or finished) under the cardboard for the worms to work in and 'till' themselves. Worms are surprisingly efficient at moving organic matter deeper into the soil profile. The cardboard also does a good job of blocking light and air from the carbon lower in the soil profile, preventing it from converting to CO2 and leaving.

If I keep the soil covered, I can easily dig as deep as I need to. If I leave off the mulch, I can't even scrape with a hoe deep enough to plant potatoes.  

 I like to collect my cardboard over months, and leave it in the rain. The rain and sun makes the plastic tape simple to remove. After the plastic is removed, I put it on the garden, often in the rain. The pre-soaking helps me put it down with less hassle and wind blowing issues than fresh dry cardboard.

I try not to till after initial bed establishment. The area of my garden that was tilled in the first year was so much harder to work than the area established with sheet mulching, that I have no desire to till, no matter how many helpful neighbours suggest I till my mulch into the soil to 'incorproate' it before planting system.

I don't think you need to shred cardboard, but to keep it moist. This way, worms will do the work for you in weeks.
Depending on your climate, you might want to bury it a little so it maintains humidity long enough to be decomposed.
If you have clay soil, it's best to work it in the wet season (but not too wet!) when you can dig it with ease.

Catie advice for removing plastic tape sounds great, too.