Now that you mention fire, I wonder if I could dig a big pit, stack them up, and make a bonfire?
That would work, I would think.

But IMHO, that would be a waste of a great compost resource. In the last few years, I have really started using all my homegrown, organic resources to make compost for my gardens. Years ago, I used to haul away all our fallen tree branches, bag up all our leaves and grass clippings and send them to the landfill or burn them at home. Now I have learned how to recycle all that stuff at home to make better compost with chickens than I used to buy in bags at the big box stores.
Maybe this is a topic for another thread, but I'm somewhat OCD about cleanliness. I've never understood how the deep bedding crowd deals with worms, coccidiosis, etc. I do envy your system though. I spend a lot of time scooping every last bit of poop.

I have never had a problem with worms, coccidiosis, etc... If I did, I imagine I would have to look at my entire system to see what needed to be changed. All I can tell you is that when I decided to get laying hens about 5 years ago, I did a lot of reading on different methods to house and care for them. I learned about using methods like deep litter and deep bedding which I had never used. Deep bedding seemed like a good system to me so that is what I went with.
Compared to how much time and effort it took me years ago to constantly clean after my birds, the deep bedding system just works so much better for me. Most of the chicken poo automagically dries out and works its way down in the deep bedding, keeping the top layer of the bedding dry and clean. If it does get soiled, I just toss more bedding litter on top of the old. I don't see the poo and there is no offensive smell if I maintain the bedding correctly.
When I first started with the deep bedding system, I used to go into the coop and fluff up the bedding with a pitchfork. That accelerated the process of the chicken poo working its way down to the lower levels. I don't even do that anymore. Sometimes, if a place needs some work, I'll just toss some chicken scratch on that area and the chickens themselves will turn over that spot, cleaning it up. But most of the time, I just add fresh litter on top of old litter about every 2 weeks all throughout my 6 months period between total coop cleanouts.
My main coop bedding has been shredder paper products for the past 2+ years. But I don't hesitate to mix in free wood chips, leaves, or dried grass. It's all natural, organic, and will make great compost. But the paper shreds, IMHO, just have advantages over even leaves and dried grass clippings. Mainly, less dusty.

If I had to clean out the coop every few days like I did years ago, I would just not have chickens anymore. Like you, I was really concerned about any and all poo in my coop. I was constantly cleaning. It was tiring for my younger self. No way do I have that energy at this stage of my life. But honestly, the dry deep bedding system keeps my coop cleaner, smells better, and my chickens are happy and healthy. That's what works for me and allows me to enjoy chickens.