Simple Bathtub Strainer 1

My 40-year-old metal bathtub strainer is corroded and broken. Retailers want about $10 to replace it, which, to me, is absurd for a piece of metal with holes in it! The drain is also corroded and "frozen" in place, so, I'm afraid to remove it with any kind of tool, lest it damage the porcelain tub (a plumber who was at my house for a different reason agreed that it was a possibility).

The drain measures 1-1/2" wide and just under 1" deep before it hits the drain's "cross".

This "thing" is 7/8" deep (i.e., the cylinder that goes into the drain) by 1.475" wide, so, it should fit with a little wiggle room (don't want to make it snug, lest the plastic scrape and break against the metal drain). The "mesh" (i.e., the part that goes on top to block the hair) is 2-7/8" wide, and, essentially, acts to prevent the "thing" from going down the drain, so to speak. The mesh is about 0.03" thick, which should enable water to flow around, under, and over it. I'm not sure that the mesh is fine en