"Firebox repair is one of the dirtiest, filthiest, most uncomfortable and awkward jobs in masonry"

James Watts 2002

There isn't anything pretty about it.
There are a few tricks that can make the job a little easier.
Since you have this tall stack for venting smoke out of the house, lets take advantage of it.
Before I start the demolition process, I wire a small household heater to the damper.
(See photo below)
Open a window in the room. With the hot air traveling up the flu most of the fine dust
and soot will be evacuated rather quickly.
As most firebox repairs are done in occupied homes, this trick will be appreciated immensely,
keeping the dust and sooty smell to a minimum.
Note. Once the heater has been used in this manner it may emit an ash like smell for some time.
A good quality dust mask is highly recommended.