I would then use a twist drill with a point and drill a series of holes that are "edge to edge" or somewhat overlapping, and then use a wide chisel to chop down the small edges that remain. It's a good idea to clamp a piece of wood as a guide along the groove so you get vertical sides and it doesn't stray.
Another option if you have an 8mm chisel or lockbettel is to chisel out the entire hole. Since you'll have an open side, it's quite easy to remove the chips.
If the grooves were to go straight through the entire beam, I would saw two grooves and then chop away the waste, but I assume you want the groove from the top side and not all the way through.
With the old beams, I will probably have to go through the whole thing since the new beam is inserted from below with the beam holders mounted.
Another challenge I realize now is that it will be tight to access between the old beams to make the cut from the side. Might have to go from below if it's going to work. 🤔
Yes, with the old beams, you'll probably have to go from underneath as you show.
One tip is that if you cut away a piece of the beam, you can use pieces of that material to glue back into the groove under the fitting, so you "hide" it fairly well.
Moreover, if you use a piece from the surface, it will hardly be noticeable.
