Single public key for NaCL signing and encryption?
Is there some safe way to sign the private key used for encryption
  with the signing keys?


What you're talking about is also commonly referred to as "keychain" or "keyrings", a concept popularized by programs like GPG, which do exactly this:
They generate one master signature key, which you securely distribute and which then "certifies" the other public keys to belong to you. This way you can keep your master key offline and only use to sign your everyday encryption public key and your everday signature public key.