Often, a swivel type clasp is used for securing cushions to the sofa proper..... in your case the plywood.
There needs to be some attaching piece(s) on the cushion (corners) to clip to. No matter what kind of DIY fix, this concept of attachment is likely your best, easiest, least expensive, most permanent, cushion-removable fix.
Probably the springs have not weakened. Rarely do I see broken springs. Most likely the spring supports have failed in some capacity, not the springs themselves. I see and fix this fairly often with older furniture. Spring support failure cause: 1) clips loosen or detach from the wood frame 2) Spring ties (string/twine) loosen or break 3) jute webbing or other banding straps loosen or its attachments (nails, staples) fail 4) a broken or loosened board (frame member, wood joint). None of these repairs are difficult, but more time consuming.... upholstery, in general, is really simple and easy work. For these internal fixes, it's just a matter of diving into the internals to access the problem..... just awkward maneuvering often times. We did a ply-sheet fix for Mom's sofa seating (spring support failure), until I fixed it later.