How to make new sling for patio chairs?

I have a set of patio chairs that have a metal frame and fabric slings like the image. The fabric is rotting out. I see that you can buy new "slings" and take the chairs apart and try to put the new fabric in place. The replacements are expensive and ugly. I'd like to just make "rectangles" of indoor/outdoor fabric and use grommets and cord to "re-seat" them. I'm thinking by having the fabric sort of wrap around the sides--and lacing up the back. Has anyone tried this? I hate to just buy new chairs when the frames are fine.
q anyone make a new cover for patio chairs, outdoor furniture, painted furniture
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