Using same keypair for Diffie-Hellman and signing
The paper "On the Joint Security of Encryption and Signature in EMV" shows that ECIES and EC-Schnorr signatures can be used together without compromising security:


  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


Ed25519 is extremely similar to EC-Schnorr, and both ECIES and Curve25519 are based on EC-DH, so this gives some indication that using both Curve25519 and Ed25519 with the same key-pair is secure.

Still a proof that directly refers to a keyexchange as used in Curve25519 would be nice.