Mine does have the control bracket the same way. In order to get mine out, I need to (while in neutral) push the lever to about 45degrees. Then I need to pull out on the back side of the control and slide it back. Once it gets into this position I think I need to pry the bottom end of it out first and then can wiggle the top control arm free.
The hole that mine is mounted in is a pretty awkward shape. I can't promise it wasn't broken at some point -- except that they didn't build your boat around the controls. They installed the controls at some point.
The trickiest part of the entire operation is to get backing nuts on the mounting bolts when it goes back in. You really need to use your bendy arms and lots of patience.
Former owner of a 1987 Supra Saltare. Current owner of a Malibu 23LSV.