I'm setting up a system to update software on a device and I would like to encrypt the update files using a private key that I have created and then decrypt them with the public key. All of the examples that I have found encrypt with the recipients public key, I want to encrypt with my private key. I have seen Bob & Alice examples that use encryption of a file with your private key and then with the recipients public key, but I can't figure out how to do the private key encryption.
This is not the way GPG works.
You encrypt a file with a public key (may be yours), and decrypt it with a private key.
So if you share your public key on the Internet, anyone would be able to encrypt a file with your public key, but you would be the only one able to decrypt it.