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I just used whatever I could find at Joanne Fabrics. It wasn't as dense as the OEM foam but worked. The stuff I bought was 1" thick, about 22" wide and on a roll about 4' long. I cut two pieces that fit perfectly in the pocket of the bottom side of the cushion and curled it at the front to match the cutout for the seat frame.
One extra step I did was cut out and glue part of an old towel to the bottom of the foam to help keep the seat frame wire from cutting through it. It did look like the OEM foam had some sort of protective cloth on the bottom for that same purpose so I tried to do the same.
I noticed the fabric when I had my cushion out. I had to glue some of the cushion back together because it had started to split in a few spots. I saw in this post that landscaping fabric is same thing as the fabric they used on the cushions. I have plenty of that. So, I used some spray (aerosol) adhesive to reinforce the back with my landscaping fabric.
Trying to mimic what you did. Attached is a picture of the underside of my seat cushion. The red boxes are where I think you described putting the extra padding. The blue boxes are "cutouts" or indentations that appear to go over the frame. I wasn't going to add padding there.
