What about GF2P8AFFINEINVQB?
The only case where I've had use of GF(2^8) inverses is in FEC algorithms (Forney's algorithm) and then you need some kind of weird polynomial. But all of those needs are rarely in the hot-path, and the FEC algo's are way outdated
I really think it's only AES since thats the only place I've seen that polynomial used. But of course maybe there's an obscure tape backup FEC algo used somewhere in datacenters?