In general I think it's a good idea to get creative like this.
In detail, I can think of a few problems with this design. Mind you this is without having tried anything similar, but I'd think that you will run into problems of comfort if it has to be bolted to the underside of your desk. Not only will that dictate seat position, but also control positions as well (if your seat is too far back you will have to hunch forward to get the joystick, or whatever.
Rather than pulling down from a higher position, I would suggest a self-mounted unit that rests on the floor.
Take the cross-arm and put it under the toes of the pedals. Mount it on a flat board. Now rig the undersides of each toe with a short downward pole to the cross-arm. You push on a pedal it pushes the arm down. The box with the servo would sit between the pedals and probably not get in the way. Then to add resistance all you need to do is put a spring between the cross-arm and the board below it (so the spring pushes the arm straight up, one spring under each tip of the cross arm).