Outdoor Living & Lifestyles - Patio Swing Web Repair

I have a stand-alone patio swing that is 3 years old. The seat cushion and awning rotted away. In it's rotting away, also rotted the stiff webbing that the seat cushion was sewn into. So, now we are left with a bar, under the knees, a bar at the vertex and a bar along the neck. What is the best way to repair this? I was thinking of using some Nylon 2" webbing and weave the strips? I'm just not sure if this is the best way to fix it or how to best attach it.
Thank you.

The frame is made of Aluminum tubing.

Can you locate the manufacturer, and call them for replacement parts? We did that with a stand alone swing we had. Otherwise, I guess just look at how the other webbing under the cushion was attached (hopefully, through holes in the aluminum), and use your idea of replacing the webbing.... BTW, I try to stay away from the big-box Home improvement stores for this type of repair, as their employees aren't always knowledgeable, and go to my local ACE hardware for advice - they have always been very knowledgeable and helpful.

Also, I have been removing my seat cushions and storing them each fall to prevent the rotting......