If you want a properly realistic result with zero distortion in the thickness of the strands of the metal meshwork then you really have to model that panel in that shape. But I don't think we do want that. In the real world a flat mesh is press deformed into the shapes required, so we should try and mimic the physical consequences of that, which will include some distortion of the perfect pattern, but no variation of wire thickness.
However, because the curvature is only slight , or at least the bits where it's not slight are only at the very edges, and mainly hidden by the frame, I suspect the distortion you'll get with something like an FFD or Mesh Deformer might be OK to get you a decent result despite a tiny amount of thickness variation that will get introduced along the way.
So, assuming this end section is likely to be made from a circular section of mesh, your first job should be to boole intersect a square section of mesh with a cylinder, and make that a single editable object. At that point you may be able to try soft selection to pull a nice curve out of the end section, or you can try it with less scope for human inconsistency with deformers, of which I think mesh deformer will be most successful, the cage object being a cylinder with about 6 cap segments.
A mesh deformer, yesterday.
On another note, you may want to fix the rogue triangles and near coincident polys that is making your main metalwork look scrappy round the edges, and I suspect we need some phong breaks there as well for truly clean, sharp cornering, especially if you are not using SDS.
CBR