How do I attach switch back box in lathe and plaster wall

[billyb_1234]

I'm installing smart modules in my light switches which means I need to replace the existing 25mm back boxes with 47mm ones. Downstairs all walls are brick and plaster so I've managed to deepen the back boxes with an SDS drill. I was expecting the same upstairs but some of the walls are lathe and plaster, and the existing box is screwed into what seems to be a structural horizontal piece of wood. This wood is not deep enough into the wall for the 47mm back box. The cavity is deep enough directly above this wood to put the back box, but it doesn't seem too secure to only fix the back box at the bottom (to the top of the wood) as pressure will be put on the box going into the wall when the switch is used. My current plan is to fix a wooden L shaped bracket to the top of the beam of wood in the wall, which would then give some wood behind the new back box to screw into. Before going ahead with this I wanted to see if anyone had come across a similar challenge with lathe and plaster and had any better suggestions.