Okay this is the $hittiest drawing, but it was on the quick.

I would make the parallel reinforcements (the blue) if the couch frame isn't that thick. I think you can make this out of framing 2x4s. Just place screws along the length it is in contact with the couch frame... maybe even add wood glue (like titebond III).
I would use angle brackets to connect the crossbeams (red) to the frame. As someone said, I would use bolts with a thread locker, not screws.
I would also attach the bottom (relative to pic) reinforcement (blue) to the outer frame of the couch, ie the frame the back legs are attached to, not the beam that supports the backrest. In most couches, the backrest frame isn't as solid as the outer frame.
Oh and try to put the transducer right under the butt of the seated person.
Finally, I would reinforce the entire outer, bottom frame with angle brackets. And by the looks of your couch legs, you will probably need some rubber feet.
Anyway, this is what I would do. Hope it helps a bit.