100% it’s the shavings. And it’s not your fault.
Bumble is caused by two things, either long periods of time on “harsh surfaces” as you put it, that causes sores, or wet conditions that grow bacteria, and a foot injury for the bacteria to get into. If you’re not spot cleaning every single day to remove wet bedding, and replacing at least weekly, it’ll happen eventually. Shavings are just terrible in general, they’re absorbent, and soak all the wetness up and keep it there, and then they’re natural fibers, too, so they’re perfect for harboring bacteria, and aside from all that, they have scent oils that are toxic to birds, even pine and aspen, and it’s not natural for them to walk on puffy stuff, it’s not good for their legs, and it’ll stick to their feet when they inevitably step in poop. When I started with quail many years ago, everyone, and I mean everyone said either shavings or wire, and they still do, so don’t blame yourself, both are terrible and people just don’t know the good alternatives yet. You mentioned paper towels and carton, so you’re on the right track. What I do, with no issues, is take a “pop-up” mosquito net meant for a bed, I use queen sizes, but I’m crazy and have plenty of space, they make “bivy” sized ones you could put on a large table, put thick puzzle exercise mats beneath for foot support, about a half inch/inch or so, and paper massage table sheets inside for a liner, weighed down with sand or beanbags. You’ll have to pull out the sheets every day. It will suck. But, your birds will be happy and healthier for it. Hope this helped.