Cardboard would be good. Actually, this past year, I flattened out old cardboard boxes that I’d collected and put them down around my tomatoes primarily, and then put pine needle* mulch on top of the cardboard. I had the “cleanest” garden EVER ... the only weed growth I got was right around the plant stalks where there was a slight gap in the cardboard ... just little small stuff that I removed when I saw it.
This fall, when I cleaned up the beds & removed the pine needles, the cardboard in many places was almost totally disintegrated. I pulled out a few of the larger pieces & they went into the compost bin ... the small pieces, I just turned into the soil. I noticed a lot of earthworms which are a very good thing in the soil.
*We have probably a dozen or more 80-90 year old pine trees on our place - they are huge! They also shed a lot of pine needles in the fall. I rake & bag them to use for mulch in the spring. The old mulch needles, when I lift them off the beds, go in the walkways between my raised beds which helps keep the weeds down there. I like to “recycle” whatever & whenever I can.
Sounds good. Final question though is what zone are you in? Here in MA active composting is limited to about 5 months.