Definitely time to reupholster.
The rouching detail at front of arms and on the upper side at top of back was made by sewing a strip of elastic to the facing, while the welt cording holds the bias of the larger plate at a certain length and stability. This way, the facing or boxing or flap or whateveryoucallit eases in, like a dress sleeve, gathering up nicely to be secured down in smaller tucks rather than large deep pleats. Even though the new fabric has more bulk than the original cotton print for this, it still looks nice for this design.
Pleats to fit the overstuffed-ness are carefully matched at inside-back as I pattern off the sofa instead of the old pieces - they are too tattered to try to template from, or even get an accurate measure. I'll have to get pictures of the happy ending of this project at a later date from the new owners. We were in such a rush to deliver on moving day that I didn't get pictures in the new setting!