Proof of NFT ownership?

I am looking at a project that relies on users being able to prove that they own a given NFT. It seems like the best course of action would be to have them sign a message with their NFT following these instructions: NFT CLI | Chia Documentation, unless there is a more elegant way.

My question comes from verifying the signed message. From the public key and signature, is it possible to determine which NFT signed the message?

it depends on what you are trying to achieve. My Software Chia NFT Minter proves that you have a given nft by checking if it is in your wallet. The NFT acts as a license for the Software.
It does so by utilizing the rpc interface of the wallet and the wallet must be running.