OK, I have a plan for this, which I think is going to produce some fairly decent results. It's based on modelling the top half.
So, for stage 1 I have done what you presumably did initially, but instead of doing it flat, I am extending it down half the depth of the mattress from either side, with the intention of avoiding the surface deformer altogether.
So that tessellating piece is going in a standard linear cloner / connect type setup to produce a suitable amount of them nicely stitched together, and then I'll be able to flatten the ends of the sheet. The crucial difference here in this edge flow versus your original is that mine remains fully planar in the direction I want to to fold, and so it can do so without any interruption to the zig pattern because there are no diamond / kite polys at 45 degrees to the fold lines. And that is going to be the key difference here I think... but as a secondary thing we also have topo at the start that is impossible to produce ngons or triangles from when later subdivided, which is also a good thing, and will keep all the modelling tools fully functional until the end of modelling...
Of course, once subdivision is involved then we will lose our carefully placed corners, and the sharpness of them, so we need to address that next. We have a number of options here, but one option we don't have is to bevel anything, which of course will destroy our overall curvature. So that leaves us with edge / point weighting or global non smoothed subdivision (with the command rather than the object) at very high level - probably 3 or 4. Experience tells me that the former is probably the best option for this project, or at least it will be faster to try than the other method, so is worth a go first.
It makes sense to do as much of this as we can while it is still a single clone, so I selected these edges for weighting, and did so to 70% with the aim of ONLY hardening the corners that need to be sharp, and not the rest of it, hence the slightly unusual selection...
So having cloned and collapsed that I have then path selected the end edge loops, and Pulled those down to match the longer sides. Then we need to cut in a single repeat of that pattern into the edges that are folded over (and weight them), giving us perfectly planar topology at the fold lines.
We could also try a smoothing deformer on the weighted mesh, to dial back the weighting in a more organic way...
Of course this is just one of many ways to approach this sort of thing. Most people are going to pop a cube in there, and then do the pattern with material displacement / normal maps if they are in a hurry, and the results they'll get from that will be pretty good.
CBR