Good job. It's a bit scary cutting into your seat, isn't it.
I've just done mine also, but not to lower it, although that was one of the consequences. I cut it to a similar shape to yours, cut out the whole of the foam underneath the butt area and added a different kind of foam, raised it a bit at the front and widened it by an inch in the sitting bone area of the seat for better support.
I also added a layer of 8mm soft smoothing foam over the top of the whole seat.
I've used your pic as a template. The straight lines are the section I cut out and the curved lines are the new width of the seat.
Tools used were scissors, electric knife and rasp. I glued it all using contact adhesive. Cost was $A60.00 for the seat foam, $A16.00 for the smoothing foam and around $A20.00 for the adhesive. I already had the staples and staple gun.