I raised thousands of birds in brooders just like this. Yes there are better systems. But if you want to restore Granny’s antique then that s a different situation entirely and it will successfully raise birds. I love my birds and antique farm goodies. Combining the two are pure heaven to me.
If it was me, and I realize it’s not, I would honestly think very hard about an alternate heat source. Good luck with it and let us know how it turns out and what you did.
You can buy the wire on eBay. I buy it for foam cutters. That being said I have no idea if that is what actually heated your brooder. There is no way to replace the asbestos that I know of. Use extreme caution here. Be parinoid about this wire and aesbestos. You can burn down a building with it...
Be careful with that “cloth” and for pity sake don’t breath any dust given off in removing it. Probably asbestos. The cloth itself is probably not the heating element. There was probably a nichrome wire inside of it that probably rusted away much like the heating elements in a cabinet incubator...