The reason is that the existing plastic soil pipe has
been damaged within the wall by heat from an adjacent
chimney. The walls are rough stone, about 2 feet thick.

Weird.

Fix the flue, not the soil pipe.
If the chimmey is leaking within the wall it could create a fire or
let fumes into the house.

#1 Dismantle the section of wall as best you can with support
#2 Rebuild the wall with fire cement around the chimney area to seal
it
#3 Use any piece of large diameter stainless tube if you wish to
sleeve the hole through the wall
#4 Fit conventional soil pipe through that sleeve with an airgap,
firemastic the inside edge leaving the outside free to vent

That way any soil pipe failure does not result in water (or worse!)
damage to the fabric of the house, underfloor areas or whatever. You
do not have to worry about trying to get a stainless steel soil pipe
of the right size or fitting (which I suspect would be extremely
expensive unless hotels use them).

I have added uk.d-i-y to the newsgroups so you get more responders.