Not 100% sure if it will fit, but I like your idea of cutting it out and installing some wire mesh instead. If you are looking to buy some high quality stuff that will last, call these guys and they can send some samples and help you out with exactly what you are looking for as far as size of the opening in the mesh and alloy/color of the mesh.
Belleville Wire Cloth Co., Inc - Woven Wire Mesh | Wire Cloth | Stainless Steel Wire Mesh | Wire Cloth Strainer
Belleville Wire Cloth Co., Inc - Woven Wire Mesh | Wire Cloth | Stainless Steel Wire Mesh | Wire Cloth Strainer