Wet sand blast. Makes a mess, but not a dusty mess, so the rest of the house isnt coated in an inch of dust.
Cost a couple of hundred quid for the day for a machine, 8 bags of sand and a local student to get filthy.
The sand, water and crap falls to the floor where you shovel it up and export. came out well. Then just got my builder neighbour in to do a bit of pointing to the brick vaulting and it looks sweet.
Obviously it’s not sealed so over time efferescence will build up again (the fine crystalline dangly powder) but you can just brush it off or hoover it off.