Trying To Figure Out How To Reupholster A Rocking Chair: a house log

We got this rocking chair for $25 thanks to craigslist, because we enjoyed the plain shape and the low back and the rich chunky wood. Plus I have been dying to add a rocker to the new house’s living area (since I feed Clara all the time while hanging out in the public part of the house, as opposed to retreating to the nursery or the bedroom). Plus she loves rocking at John’s mom’s house, so we thought it would contribute to good quality time with the bean. But this rocker is obviously lacking a bit in the seat and back cushion area. No worries, we simply figured we will reupholster it.

Until we realized that we had no earthly idea how to attack the double sided back cushion. As for the seat, we are planning to remove the boards that make up the bottom, add a foam cushion, staple batting around the back to hold it down/smooth it out, and reupholster that the same way we’d do any removable chair seat (and then screw it back in from the bottom). But the back has us stumped with a capital um.

If you remove the fabric you can see right through the chair. In other words there are two upholstered panels on each side that were likely stapled and then trim was used to cover the staples, but we are not sure if we should add some structure so it is not simply fabric that supports a person’s weight against the back. That seems like it could sag over time, right? Any ideas? We have seen that seat-belt looking stuff that you can weave to create support and we are wondering if we need to do something like that for the back (so people can lean on the chair without feeling like they are falling into a hole) and then somehow attach two more fabric panels on either side of it (you know, for a seat-belt sandwich?). Can you tell we have no idea what we are doing?

Somebody assist us!