Dor,
Tarp for the treated lumber you will use for the bed frame?
Why do you want to cover the treated lumber? Is it because it was treated and you don’t want it to seep into the soil? As far as newspaper, I would only recommend reading up on your specific local (?) papers. All the ones I have accesses to are made from soy (use soy for the ink) and it never really breaks down completely. (Not considered organic here)
Shredded will take even wayyyyyy longer.
May I suggest just using a landscape fabric that is sorta like plastic. I bought it to keep my pond area clear of growth. It works wonderfully and lets the ground breath somewhat, it has teeny holes and the water will drain eventually. I fear actually plastic will retain water.
And if you have holes grass may come up though the holes.(depends on the kind of grass you have. My neighbor (behind me) has grass that will (does) travel until it finds a place to light then grow.) You can also use unprinted cardboard. I know that will work.
How many beds are you planning? What size? Long, wide and high?
You may not need to remove the sod. If you really want to; just a shovel deep turn upside down.
Tires work fine. I tried 4different ways of a set up. Some had actual heavy plastic (bags mulch came in) overlapped, doubled and secured to keep the soil and water from running out, garbage bags inserted, with and without holes and one with just plastic where the tires met in the pile up. I had at first 2high then I went 3high when I was told I needed new tires by the SALESMAN. Keep in mind they will absorb the sun and keep plant and soil slightly hotter then your ground soil. Also they may hold the water in the insides of the actual tire. Make sure you fill the tire sides with soil that will not retain water, don’t want to mold your roots.
The black rubber will retain the heat!
Also back to the strip in the pic.I would give a few inches of breathing room for your fence. Not sure if you get Downpours or not but if you do, you sure don’t want to keep that fence retaining water.
Any questions or thoughts, I will keep track of this thread.
I am racing time and trying to work around weather, doing several projects ..But. I will be here.
Hope I helped you some!
OH, I posted the write up on Soy I found years ago, I did a few searches and can't find it here.If you need it I have it in a word doc.I can post it.
Kale