Use the chimney as a trash chute of course. If you got a hand truck/horizontal dolly, you can put a large plastic container (think mid height storage containers) on top of the dolly and push it inside the chimney to make cleanup easier. Some cardboard laying in the bottom of the plastic container will soften the impact of demolished material and prolong the container integrity and life. About 3/4" thick of cardboard worth from the attic, and an additional 0.5" thicker for each floor more than one (yes it's over kill). Replace as necessary, and always before the bottom layer is damaged, including being crushed. If it's crushed but not torn/penetrated, put that layer on top of a new cardboard stack.

And if you don't have a hand truck, it's worth the investment for any home. You don't use it every month, or perhaps year, but damn does it save your back!

Mulching flowerbeds? Throw the bags on the dolly. Tearing out a concrete foundation home play set? Chain link fence? A hideous looking rock garden? Invasive hedge rows? Did the creek in your backyard flood and deposit driftwood? Throw that shit in the dolly. Hand trucks are easier than using a wheel barrow to transport to the dumpster or whatever. Just get 6" castors/wheels or larger for outdoors, and 3 or 4" castors for indoors, with the thickest rubber you can find for longevity. A wider wheel works better in irrigated/wet lawns than a narrow one of course. Also, don't buy a plastic hand truck; get all metal parts excluding tires.

Now I'm thinking about using my hand truck to carry groceries inside with one trip. Maybe I can start using it weekly! The possibilities of use are endless, really. My hand truck is older than I am too.

Furthermore, do you run a bar or venue? There are keg dollies with a curved skeleton to safely move 1/2 barrel kegs from storage to tap. Some even have an adjustable gravity latch to lock the keg in place for smooth handling.

Paid for by Big Hand Truck Manufacturing of America. /s

This reads like a newspaper consumer op-ed. It ain't. Just a fan of not fucking my back up anymore than it already is. Get a 2 in 1 hand truck dolly. You'll thank yourself for it.

It is very difficult to comment here effectively without a site visit. When joists rest on ledges around a chimney they are surely doing some “work” structurally. Starting in the attic and working your way down you will quickly find out what the chimney is really holding.

> added to support weight

I doubt it. The chimney is the last thing you want as a structural support for joists or rafters. If anything, you want as little wood touching it as possible because of the fire risk.

Bit by bit disassembly is the way you'll see if it's supporting anything important.