I wish I had taken some photos of my process but alas, I did not.
There are two separate and distinct kinds of springs in our seats.
The first is the zig-zag style, also known in the industry as "no sag" springs. See photo, though I don't know if the dimensions match ours, but the pattern is identical. These springs are affixed to the seat frame by spot welding. They come in a number of different dimensions and duties. Mine were all fine, so what I did was double up on the springs and used hog rings and a crimping tool to bolster the effectiveness of the existing springs. I doubled up on all of them and even added two at a cross ways bias. Using my hand pressure as a crude gauge, it felt like I had added quite a bit of stiffness to the overall springing. No; it was all an illusion.
The other spring is the flat spring, and these are custom to this seat.
Despite my laborious effort in adding stiffer and more springing with the zig zag, the effect of all my labor was about nil. The seat still totally bottomed out even with my lightweight young daughter sitting on the seat in testing.
The pool noodle addition did the trick. That prevents the seat from bottoming out and damps and adds effectiveness to the springing that's there.