Are there signatures that don't have subliminal channels? Are there signatures that don't have subliminal channels and also don't require commitments or zero-knowledge proofs?

DSA or Schnorr signatures need a nonce which can leak valuable information. There are derandomization schemes, but the verifier can't check that the signer used them without extra steps.

Is there a signature that avoids these problems?
According to this answer, RSA with the "usual" "padding scheme, described in PKCS#1 as the

'old-style, v1.5' padding," can be made to satisfy that; one would need to specify NULL or omission

and require that the public exponent's prime factors are all easily

findable and sufficiently bigger than the 4th root of the modulus.