On 11/07/2020 20:53:08, NY wrote:

The sparking plug was coated in a thin layer of
black carbon, but the gap looked OK and there was no coking-up of the
contacts - I cleaned the carbon off the underside of the tag and the end
of the rod (ie the surfaces between which the spark jumps) but that
didn't help either.

Sooted spark plug does suggest carburation issues.

I've got it to a state where the mower will usually run for tens of
minutes, with irregular misfiring and occasional backfires, but will
suddenly stall without warning, usually when cutting short sparse grass,
rather than when it's working harder to cut denser or longer grass.

Which suggests mixture is perhaps closer to stoichiometric with higher
loads.

Does it tick over / idle without misfiring?

I would be tempted to follow the Youtube video for servicing the
carburettor that has been posted on this thread.