It does matter if you don't want wet, rotting paper and associated mold perpetually in your bilge.
Plywood will be the first choice, what would be the second?
I agree that a chopper gun may be the most well-established solution, but there has to be other outside the box solutions that are comparable. Recycled plastics sell for cents per pound polyester resin has compressive and shear strengths 10x that required for a core material. Do they make a hopper gun that shoots plastic pellets? Something like the popcorn ceiling guns?
This post from long ago in the thread was a grand hope. I did not comment because I hate to rain on hope.
The trouble with plastic is that plastic is a generic term for many arrangements of chemicals. And plastics are not friendly to each other. I worked in plastics for a few years and we couldn't even recycle our own product back into itself easily, fully, well. We were able to use our recycled plastic in the core, ironically. The problem was the inks used messed with the colors and the extrusion really would only cooperate to a degree of reintroduction of about 10%. When we put a new extruder online; initial setup falldown was massive and we had to rent an old warehouse to store it all. Basically, miles of plastic waiting to go back into core at a rate of 10% of about 40% of the total or 4% reintroduction only. I did some analysis of how long it would take and to see if it was cheaper to rent or dispose. It was cheaper to dispose, but the company actually wanted to do the right thing. And we used it as a chip for the rental rate for an unised building.
Core materials need to be consistent is my point I suppose. You can't just mix up a bunch of plastics and get them to process easily. The process of refining recyclables is its own process.
The Andersen Window Corp wanted to reduce vinyl/wood wastes. So they ground it all up and ran it through density separators. Giant vibrating tables that operate at a certain frequency so the grindings go into different conveyors and hoppers. The process was good, but the vinyl still had bits of wood on it. So, they ground it again and made a wood/vinyl material that is actually wood and pvc combined. Yeah, I said it.
Anyhow, fpj is probably feeling a little beat down by the forum, so I thought I'd throw him a bone.
I am not sure how the wood and pvc would behave as a core, but lighter with lower absorption of water rates, etc. than wood alone.
But you asked for the second cheapest core and I would say wood combined with recycled plastic/vinyl would probably be it.
The reason we don't have it is the research required to refine the recyclables and then grind it all into a core and then determine a way to extrude it is certainly not easy stuff. And the capital costs are way high for it. There is probably quite a bit of research going on now with the plastics glut. One would
hope.