Using a single Ed25519 key for encryption and signature
The paper On the Joint Security of Encryption and Signature in EMV is very close. Section 4.4, "On the Joint Security of ECIES and EC-Schnorr", states the following result:


  Theorem 2. In the random oracle model ECIES-KEM and EC-Schnorr are jointly secure if the gap-DLP problem and gap-DH problem are both hard.


Obviously, this does not apply to EdDSA/DH out of the box: ECIES is a certain application of Diffie-Hellman, and EdDSA is a slightly modified variant of elliptic-curve Schnorr signatures.
However, the proof sketches in the paper should be easily adaptable to EdDSA combined with any other reasonable Diffie-Hellman incarnation. (The details of this depend a little on how the DH shared secret is used for symmetric (authenticated) encryption, but it seems possible to modify the proof for all realistic settings.)