Just a thought, hard to see with only pictures and not being there, but-
Notch out your new bracket to go around the PS bracket.
Make a custom washer(a big one) for the PS bolt that can cover both the PS bracket, and the part you notched out around the bottom of your new one and use that bolt to pinch both brackets in place. Then use the additional bolt on the new bracket as you describe as well.
This would be provided both brackets are the same thickness in that area.
Alternative, and more difficult, splice/weld the two together. This would require some precision. Removal of material, weld, grind flat, have it re-powder coated or sand blast/prime/repaint.
Not sure exactly how it looks but you might be able to remove the end of the PS bracket and drill a hole in the new bracket if you go this route, vs notching out the new bracket.