light a smoky fire for a day or two to get rid of a week-old colony?
Way too late: smoke may persuade a swarm to leave in the first half hour, but once it's laid down comb - and they get to work pdq - it's a nest, and you can forget it.
Risky putting smoke into any sort of nest: a spark may ignite dust near beeswax, and once that starts...
Years ago I took a street tree swarm that had come from a chimney nest, and residents gathered to enjoy the fun; at some point the chimney owner told me his bedroom carpet was soaked with honey. Up we went for a look, and sure enough, in the heatwave combs had melted and wax and honey had run down the chimney, out of the fireplace and over his bedroom carpet.
blocked off up top with mesh after emptying a can on Raid into it?
Raid uses chemicals such as pyrethroids - cypermethrin, imiprothrin, and pyrethrin - and I cannot fathom why anyone would recommend using it on or near honey bees or any other pollinators.
pest controller had told her she'd have to get the chimney dismantled
Correct, and that is when the true cost appears: scaffolding, and operatives with a combination of beekeeping & building skills. There are a few companies that specialise in this work, but trust me, the bill will be staggering: likely £6-10k.
I charged £600 for a job that took 1.5 days to remove a nest from inside a bedroom ceiling. By comparison, a firm with beekeeping & building skills quoted £4.5k, which the client could never have afforded. Building work involved cutting out a section of plasterboard 1m x 400mm.
block off the lower end and live with them
Good idea.