The payee can scan for transactions by checking if his private key can decrypt the metadata.
How does the payee get at the stealth private key that can
spend Q' in this scenario?
The decrypted metadata will contain the shared secret necessary to calculate it obviously. Even though it's a random number generated by the payer, it still works as a shared secret because both parties know what it is but no one else does.
But can you generate a valid stealth keypair from
combining the random number with the payees original keypair,
i.e by what procedure do you replace the ephem keypair with
just one number?
And in the scenario mentioned by my edit, the payee would first need to calculate the decryption key by multiplying his private key with the private key of the payer, as usual. Then he can decrypt the metadata and figure out the shared secret, or second shared secret if you will.
I think you mean the payer multiplies his private key with the public key
of the payee? He can't have the private key of the other party.