If I'm not mistaken, my '98 has an aluminum heat shield above the muffler. No rust, but the mounting points were cracking.
I took a peek under a early model wrangler parked in my neighborhood and it has a heat shield attached to the body above the muffler like yours. Mine does not and doesn't have any attachment points either, probably got removed when I replaced the floor pans.
Found this YJ heat shield that looks very similar to what I saw, cannot find a TJ version but I could probably make this work. Or I could go with the shield that straps on the muffler (linked above) but I dont know if that would work as well. Does the link below look like what you have?
YJ Heat shield
Also considering this, its bigger and I could trim/bend it to make it fit, also cheaper.
JK heat shield